Algebra

Edited by Nemi Boris Pelgrom (Ludwig Maximilians Universität, München)
Related

Contents
176 found
Order:
1 — 50 / 176
  1. Algunos tópicos de Lógica matemática y los Fundamentos de la matemática.Franklin Galindo - manuscript
    En este trabajo matemático-filosófico se estudian cuatro tópicos de la Lógica matemática: El método de construcción de modelos llamado Ultraproductos, la Propiedad de Interpolación de Craig, las Álgebras booleanas y los Órdenes parciales separativos. El objetivo principal del mismo es analizar la importancia que tienen dichos tópicos para el estudio de los fundamentos de la matemática, desde el punto de vista del platonismo matemático. Para cumplir con tal objetivo se trabajará en el ámbito de la Matemática, de la Metamatemática y (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  2. The construction of transfinite equivalence algorithms.Han Geurdes - manuscript
    Context: Consistency of mathematical constructions in numerical analysis and the application of computerized proofs in the light of the occurrence of numerical chaos in simple systems. Purpose: To show that a computer in general and a numerical analysis in particular can add its own peculiarities to the subject under study. Hence the need of thorough theoretical studies on chaos in numerical simulation. Hence, a questioning of what e.g. a numerical disproof of a theorem in physics or a prediction in numerical (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  3. The English Algebra of Logic in the 19th Century.Roman Murawski - unknown - Poznan Studies in the Philosophy of the Sciences and the Humanities 98:245-269.
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  4. Who’s afraid of mathematical diagrams?Silvia De Toffoli - forthcoming - Philosophers' Imprint.
    Mathematical diagrams are frequently used in contemporary mathematics. They are, however, widely seen as not contributing to the justificatory force of proofs: they are considered to be either mere illustrations or shorthand for non-diagrammatic expressions. Moreover, when they are used inferentially, they are seen as threatening the reliability of proofs. In this paper, I examine certain examples of diagrams that resist this type of dismissive characterization. By presenting two diagrammatic proofs, one from topology and one from algebra, I show that (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  5. The relevance logic of Boolean groups.Yale Weiss - 2023 - Logic Journal of the IGPL 31 (1):96-114.
    In this article, I consider the positive logic of Boolean groups (i.e. Abelian groups where every non-identity element has order 2), where these are taken as frames for an operational semantics à la Urquhart. I call this logic BG. It is shown that the logic over the smallest nontrivial Boolean group, taken as a frame, is identical to the positive fragment of a quasi-relevance logic that was developed by Robles and Méndez (an extension of this result where negation is included (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  6. Introduction to Neutrosophic Restricted SuperHyperGraphs and Neutrosophic Restricted SuperHyperTrees and several of their properties.Masoud Ghods, Zahra Rostami & Florentin Smarandache - 2022 - Neutrosophic Sets and Systems 50 (1):480-487.
    In this article, we first provide a modified definition of SuperHyperGraphs (SHG) and we call it Restricted SuperHyperGraphs (R-SHG). We then generalize the R-SHG to the neutrosophic graphs and then define the corresponding trees. In the following, we examine the Helly property for subtrees of SuperHyperGraphs.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  7. The SuperHyperFunction and the Neutrosophic SuperHyperFunction (revisited again).Florentin Smarandache - 2022 - Neutrosophic Sets and Systems 49 (1):594-600.
    In this paper, one recalls the general definition of the SuperHyperAlgebra with its SuperHyperOperations and SuperHyperAxioms [2, 6]. Then one introduces for the first time the SuperHyperTopology and especially the SuperHyperFunction and Neutrosophic SuperHyperFunction. One gives a numerical example of a Neutro-SuperHyperGroup.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  8. Introducción a la Super-Hiper-Álgebra y la Super-HiperÁlgebra Neutrosófica.Florentin Smarandache - 2022 - Neutrosophic Computing and Machine Learning 20 (1):1-6.
    In this article, the concepts of Nth Power Set of a Set, Super-Hyper-Oper-Operation, Super-Hyper-Axiom, SuperHyper-Algebra, and their corresponding Neutrosophic Super-Hyper-Oper-Operation, Neutrosophic Super-Hyper-Axiom and Neutrosophic Super-Hyper-Algebra are reviewed. In general, in any field of knowledge, really what are found are Super-HyperStructures (or more specifically Super-Hyper-Structures (m, n)).
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  9. Introduction to SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra.Florentin Smarandache - 2022 - Journal of Algebraic Hyperstructures and Logical Algebras 3 (2):17-24.
    In this paper we recall our concepts of n th-Power Set of a Set, SuperHyperOperation, SuperHyperAxiom, SuperHyperAlgebra, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one actually encounters SuperHyperStructures (or more accurately (m, n)- SuperHyperStructures).
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  10. On Some NeutroHyperstructures.Madeleine Al-Tahan, Bijan Davvaz, Florentin Smarandache & Osman Anis - 2021 - Symmetry 13 (4):1-12.
    Neutrosophy, the study of neutralities, is a new branch of Philosophy that has applications in many different fields of science. Inspired by the idea of Neutrosophy, Smarandache introduced NeutroAlgebraicStructures (or NeutroAlgebras) by allowing the partiality and indeterminacy to be included in the structures’ operations and/or axioms.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  11. NeutroOrderedAlgebra: Applications to Semigroups.Madeleine Al-Tahan, Florentin Smarandache & Bijan Davvaz - 2021 - Neutrosophic Sets and Systems 39 (1):133-147.
    Starting with a partial order on a NeutroAlgebra, we get a NeutroStructure. The latter if it satisfies the conditions of NeutroOrder, it becomes a NeutroOrderedAlgebra. In this paper, we apply our new defined notion to semigroups by studying NeutroOrderedSemigroups. More precisely, we define some related terms like NeutrosOrderedSemigroup, NeutroOrderedIdeal, NeutroOrderedFilter, NeutroOrderedHomomorphism, etc., illustrate them via some examples, and study some of their properties.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  12. Denseness results in the theory of algebraic fields.Sylvy Anscombe, Philip Dittmann & Arno Fehm - 2021 - Annals of Pure and Applied Logic 172 (8):102973.
    We study when the property that a field is dense in its real and p-adic closures is elementary in the language of rings and deduce that all models of the theory of algebraic fields have this property.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  13. Why Did Weyl Think That Emmy Noether Made Algebra the Eldorado of Axiomatics?Iulian D. Toader - 2021 - Hopos: The Journal of the International Society for the History of Philosophy of Science 11 (1):122-142.
    This paper argues that Noether's axiomatic method in algebra cannot be assimilated to Weyl's late view on axiomatics, for his acquiescence to a phenomenological epistemology of correctness led Weyl to resist Noether's principle of detachment.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  14. Choice-free stone duality.Nick Bezhanishvili & Wesley H. Holliday - 2020 - Journal of Symbolic Logic 85 (1):109-148.
    The standard topological representation of a Boolean algebra via the clopen sets of a Stone space requires a nonconstructive choice principle, equivalent to the Boolean Prime Ideal Theorem. In this article, we describe a choice-free topological representation of Boolean algebras. This representation uses a subclass of the spectral spaces that Stone used in his representation of distributive lattices via compact open sets. It also takes advantage of Tarski’s observation that the regular open sets of any topological space form a Boolean (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  15. Genealogy of Algorithms: Datafication as Transvaluation.Virgil W. Brower - 2020 - le Foucaldien 6 (1):1-43.
    This article investigates religious ideals persistent in the datafication of information society. Its nodal point is Thomas Bayes, after whom Laplace names the primal probability algorithm. It reconsiders their mathematical innovations with Laplace's providential deism and Bayes' singular theological treatise. Conceptions of divine justice one finds among probability theorists play no small part in the algorithmic data-mining and microtargeting of Cambridge Analytica. Theological traces within mathematical computation are emphasized as the vantage over large numbers shifts to weights beyond enumeration in (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  16. Algebraic and topological semantics for inquisitive logic via choice-free duality.Nick Bezhanishvili, Gianluca Grilletti & Wesley H. Holliday - 2019 - In Rosalie Iemhoff, Michael Moortgat & Ruy de Queiroz (eds.), Logic, Language, Information, and Computation. WoLLIC 2019. Lecture Notes in Computer Science, Vol. 11541. Springer. pp. 35-52.
    We introduce new algebraic and topological semantics for inquisitive logic. The algebraic semantics is based on special Heyting algebras, which we call inquisitive algebras, with propositional valuations ranging over only the ¬¬-fixpoints of the algebra. We show how inquisitive algebras arise from Boolean algebras: for a given Boolean algebra B, we define its inquisitive extension H(B) and prove that H(B) is the unique inquisitive algebra having B as its algebra of ¬¬-fixpoints. We also show that inquisitive algebras determine Medvedev’s logic (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  17. Algebraic structures of neutrosophic triplets, neutrosophic duplets, or neutrosophic multisets.Florentin Smarandache, Xiaohong Zhang & Mumtaz Ali (eds.) - 2018 - Basel: MDPI.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  18. Algebraic structures of neutrosophic triplets, neutrosophic duplets, or neutrosophic multisets. Volume I.Florentin Smarandache, Xiaohong Zhang & Mumtaz Ali - 2018 - Basel, Switzerland: MDPI. Edited by Florentin Smarandache, Xiaohong Zhang & Mumtaz Ali.
    The topics approached in the 52 papers included in this book are: neutrosophic sets; neutrosophic logic; generalized neutrosophic set; neutrosophic rough set; multigranulation neutrosophic rough set (MNRS); neutrosophic cubic sets; triangular fuzzy neutrosophic sets (TFNSs); probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; neutro-homomorphism; neutrosophic computation; quantum computation; neutrosophic association rule; data mining; big data; oracle Turing machines; recursive enumerability; oracle computation; interval number; dependent degree; possibility degree; power aggregation operators; multi-criteria group decision-making (MCGDM); expert set; soft sets; LA-semihypergroups; single valued (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  19. On the Interpretations of the History of Diophantine Analysis: A Comparative Study of Alternate Perspectives.Ioannis M. Vandoulakis - 2018 - Ganita Bharati 40 (3):115-152.
    Essay Review of “Les Arithmétiques de Diophante. Lecture historique et mathématique” by Roshdi Rashed and Christian Houzel, and Histoire de l’analyse diophantienne classique : d’Abū Kamil à Fermat by Roshdi Rashed.
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  20. ‘Chasing’ the diagram—the use of visualizations in algebraic reasoning.Silvia de Toffoli - 2017 - Review of Symbolic Logic 10 (1):158-186.
    The aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that one (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   17 citations  
  21. Álgebras booleanas, órdenes parciales y axioma de elección.Franklin Galindo - 2017 - Divulgaciones Matematicas 18 ( 1):34-54.
    El objetivo de este artículo es presentar una demostración de un teorema clásico sobre álgebras booleanas y ordenes parciales de relevancia actual en teoría de conjuntos, como por ejemplo, para aplicaciones del método de construcción de modelos llamado “forcing” (con álgebras booleanas completas o con órdenes parciales). El teorema que se prueba es el siguiente: “Todo orden parcial se puede extender a una única álgebra booleana completa (salvo isomorfismo)”. Donde extender significa “sumergir densamente”. Tal demostración se realiza utilizando cortaduras de (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  22. A Survey of Geometric Algebra and Geometric Calculus.Alan Macdonald - 2017 - Advances in Applied Clifford Algebras 27:853-891.
    The paper is an introduction to geometric algebra and geometric calculus for those with a knowledge of undergraduate mathematics. No knowledge of physics is required. The section Further Study lists many papers available on the web.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  23. Philosophy of the Matrix.A. C. Paseau - 2017 - Philosophia Mathematica 25 (2):246-267.
    A mathematical matrix is usually defined as a two-dimensional array of scalars. And yet, as I explain, matrices are not in fact two-dimensional arrays. So are we to conclude that matrices do not exist? I show how to resolve the puzzle, for both contemporary and older mathematics. The solution generalises to the interpretation of all mathematical discourse. The paper as a whole attempts to reinforce mathematical structuralism by reflecting on how best to interpret mathematics.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  24. Boolean Algebras in Visser Algebras.Majid Alizadeh, Mohammad Ardeshir & Wim Ruitenburg - 2016 - Notre Dame Journal of Formal Logic 57 (1):141-150.
    We generalize the double negation construction of Boolean algebras in Heyting algebras to a double negation construction of the same in Visser algebras. This result allows us to generalize Glivenko’s theorem from intuitionistic propositional logic and Heyting algebras to Visser’s basic propositional logic and Visser algebras.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  25. Imagination in mathematics.Andrew Arana - 2016 - In Amy Kind (ed.), Routledge Handbook on the Philosophy of Imagination. Routledge. pp. 463-477.
    This article will consider imagination in mathematics from a historical point of view, noting the key moments in its conception during the ancient, modern and contemporary eras.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  26. Christopher Hollings, Mathematics across the Iron Curtain: A History of the Algebraic Theory of Semigroups. Providence, RI: American Mathematical Society, 2014. Pp. xi + 441. ISBN 978-1-4704-1493-1. £79.95. [REVIEW]Michael J. Barany - 2016 - British Journal for the History of Science 49 (1):140-141.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  27. Arithmetic, Mathematical Intuition, and Evidence.Richard Tieszen - 2015 - Inquiry: An Interdisciplinary Journal of Philosophy 58 (1):28-56.
    This paper provides examples in arithmetic of the account of rational intuition and evidence developed in my book After Gödel: Platonism and Rationalism in Mathematics and Logic . The paper supplements the book but can be read independently of it. It starts with some simple examples of problem-solving in arithmetic practice and proceeds to general phenomenological conditions that make such problem-solving possible. In proceeding from elementary ‘authentic’ parts of arithmetic to axiomatic formal arithmetic, the paper exhibits some elements of the (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  28. The Nature of Local/Global Distinctions, Group Actions and Phases: A Sheaf=Theoretic Approach to Quantum Geometric Spectra.Elias Zafiris - 2015 - In Vera Bühlmann, Ludger Hovestadt & Vahid Moosavi (eds.), Coding as Literacy - Metalithicum IV. Basel: BIRKHÄUSER. pp. 172-186.
  29. Algebraic functions in quasiprimal algebras.Miguel Campercholi & Diego Vaggione - 2014 - Mathematical Logic Quarterly 60 (3):154-160.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  30. On pseudo-equality algebras.Lavinia Corina Ciungu - 2014 - Archive for Mathematical Logic 53 (5-6):561-570.
    Recently, a new algebraic structure called pseudo-equality algebra has been defined by Jenei and Kóródi as a generalization of the equality algebra previously introduced by Jenei. As a main result, it was proved that the pseudo-equality algebras are term equivalent with pseudo-BCK meet-semilattices. We found a gap in the proof of this result and we present a counterexample and a correct version of the theorem. The correct version of the corresponding result for equality algebras is also given.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  31. Finitistic Arithmetic and Classical Logic.Mihai Ganea - 2014 - Philosophia Mathematica 22 (2):167-197.
    It can be argued that only the equational theories of some sub-elementary function algebras are finitistic or intuitive according to a certain interpretation of Hilbert's conception of intuition. The purpose of this paper is to investigate the relation of those restricted forms of equational reasoning to classical quantifier logic in arithmetic. The conclusion reached is that Edward Nelson's ‘predicative arithmetic’ program, which makes essential use of classical quantifier logic, cannot be justified finitistically and thus requires a different philosophical foundation, possibly (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  32. Finite Methods in Mathematical Practice.Peter Schuster & Laura Crosilla - 2014 - In Godehard Link (ed.), Formalism and Beyond: On the Nature of Mathematical Discourse. De Gruyter. pp. 351-410.
    In the present contribution we look at the legacy of Hilbert's programme in some recent developments in mathematics. Hilbert's ideas have seen new life in generalised and relativised forms by the hands of proof theorists and have been a source of motivation for the so--called reverse mathematics programme initiated by H. Friedman and S. Simpson. More recently Hilbert's programme has inspired T. Coquand and H. Lombardi to undertake a new approach to constructive algebra in which strong emphasis is laid on (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  33. SOFT NEUTROSOPHIC ALGEBRAIC STRUCTURES AND THEIR GENERALIZATION, Vol. 2.Florentin Smarandache, Mumtaz Ali & Muhammad Shabir - 2014 - Columbus, OH, USA: Educational Publisher.
    In this book we define some new notions of soft neutrosophic algebraic structures over neutrosophic algebraic structures. We define some different soft neutrosophic algebraic structures but the main motivation is two-fold. Firstly the classes of soft neutrosophic group ring and soft neutrosophic semigroup ring defined in this book is basically the generalization of two classes of rings: neutrosophic group rings and neutrosophic semigroup rings. These soft neutrosophic group rings and soft neutrosophic semigroup rings are defined over neutrosophic group rings and (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  34. SOFT NEUTROSOPHIC ALGEBRAIC STRUCTURES AND THEIR GENERALIZATION, Vol. 1.Florentin Smarandache, Mumtaz Ali & Muhammad Shabir - 2014 - Columbus, OH, USA: Educational Publisher.
    In this book the authors introduced the notions of soft neutrosophic algebraic structures. These soft neutrosophic algebraic structures are basically defined over the neutrosophic algebraic structures which means a parameterized collection of subsets of the neutrosophic algebraic structure. For instance, the existence of a soft neutrosophic group over a neutrosophic group or a soft neutrosophic semigroup over a neutrosophic semigroup, or a soft neutrosophic field over a neutrosophic field, or a soft neutrosophic LA-semigroup over a neutrosophic LAsemigroup, or a soft (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  35. Mathematical Forms and Forms of Mathematics: Leaving the Shores of Extensional Mathematics.Jean-Pierre Marquis - 2013 - Synthese 190 (12):2141-2164.
    In this paper, I introduce the idea that some important parts of contemporary pure mathematics are moving away from what I call the extensional point of view. More specifically, these fields are based on criteria of identity that are not extensional. After presenting a few cases, I concentrate on homotopy theory where the situation is particularly clear. Moreover, homotopy types are arguably fundamental entities of geometry, thus of a large portion of mathematics, and potentially to all mathematics, at least according (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  36. Frontal Operators in Weak Heyting Algebras.Sergio A. Celani & Hernán J. San Martín - 2012 - Studia Logica 100 (1-2):91-114.
    In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [ 10 ]. A frontal operator in a weak Heyting algebra A is an expansive operator τ preserving finite meets which also satisfies the equation $${\tau(a) \leq b \vee (b \rightarrow a)}$$, for all $${a, b \in A}$$. These operators were studied from an algebraic, logical and topological point of view by Leo Esakia (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  37. Notes on Groups and Geometry, 1978-1986.Steven H. Cullinane - 2012 - Internet Archive.
    Typewritten notes on groups and geometry.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  38. Newton and Hamilton: In defense of truth in algebra.Janet Folina - 2012 - Southern Journal of Philosophy 50 (3):504-527.
    Although it is clear that Sir William Rowan Hamilton supported a Kantian account of algebra, I argue that there is an important sense in which Hamilton's philosophy of mathematics can be situated in the Newtonian tradition. Drawing from both Niccolo Guicciardini's (2009) and Stephen Gaukroger's (2010) readings of the Newton–Leibniz controversy over the calculus, I aim to show that the very epistemic ideals that underpin Newton's argument for the superiority of geometry over algebra also motivate Hamilton's philosophy of algebra. Namely, (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  39. Algebraic symbolism in medieval Arabic algebra.Jeffrey A. Oaks - 2012 - Philosophica 87 (4):27-83.
  40. Neutrosophic Super Matrices and Quasi Super Matrices.Florentin Smarandache & W. B. Vasantha Kandasamy - 2012 - Columbus, OH, USA: Zip Publishing.
    In this book authors study neutrosophic super matrices. The concept of neutrosophy or indeterminacy happens to be one the powerful tools used in applications like FCMs and NCMs where the expert seeks for a neutral solution. Thus this concept has lots of applications in fuzzy neutrosophic models like NRE, NAM etc. These concepts will also find applications in image processing where the expert seeks for a neutral solution.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  41. Some new results on decidability for elementary algebra and geometry.Robert M. Solovay, R. D. Arthan & John Harrison - 2012 - Annals of Pure and Applied Logic 163 (12):1765-1802.
    We carry out a systematic study of decidability for theories of real vector spaces, inner product spaces, and Hilbert spaces and of normed spaces, Banach spaces and metric spaces, all formalized using a 2-sorted first-order language. The theories for list turn out to be decidable while the theories for list are not even arithmetical: the theory of 2-dimensional Banach spaces, for example, has the same many-one degree as the set of truths of second-order arithmetic.We find that the purely universal and (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  42. Supermodular Lattices.Iqbal Unnisa, W. B. Vasantha Kandasamy & Florentin Smarandache - 2012 - Columbus, OH, USA: Educational Publisher.
    In lattice theory the two well known equational class of lattices are the distributive lattices and the modular lattices. All distributive lattices are modular however a modular lattice in general is not distributive. In this book, new classes of lattices called supermodular lattices and semi-supermodular lattices are introduced and characterized.
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  43. Caal: Categorical Abstract Algebraic Logic: Coordinatization Is Algebraization.George Voutsadakis - 2012 - Reports on Mathematical Logic:125-145.
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  44. De Morgan Heyting algebras satisfying the identity xn ≈ x.Valeria Castaño & Marcela Muñoz Santis - 2011 - Mathematical Logic Quarterly 57 (3):236-245.
    In this paper we investigate the sequence of subvarieties equation imageof De Morgan Heyting algebras characterized by the identity xn ≈ x. We obtain necessary and sufficient conditions for a De Morgan Heyting algebra to be in equation image by means of its space of prime filters, and we characterize subdirectly irreducible and simple algebras in equation image. We extend these results for finite algebras in the general case equation image. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  45. Algebraic Structures using Super Interval Matrices.W. B. Vasantha Kandasamy & Florentin Smarandache - 2011 - Columbus, OH, USA: Educational Publisher.
    In this book authors for the first time introduce the notion of super interval matrices using special intervals. The advantage of using super interval matrices is that one can build only one vector space using m × n interval matrices, but in case of super interval matrices we can have several such spaces depending on the partition on the interval matrix.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  46. Linear and Geometric Algebra.Alan MacDonald - 2011 - North Charleston, SC: CreateSpace.
    This textbook for the second year undergraduate linear algebra course presents a unified treatment of linear algebra and geometric algebra, while covering most of the usual linear algebra topics. -/- Geometric algebra and its extension to geometric calculus simplify, unify, and generalize vast areas of mathematics that involve geometric ideas. Geometric algebra is an extension of linear algebra. The treatment of many linear algebra topics is enhanced by geometric algebra, for example, determinants and orthogonal transformations. And geometric algebra does much (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  47. Superatomic Boolean algebras constructed from strongly unbounded functions.Juan Carlos Martínez & Lajos Soukup - 2011 - Mathematical Logic Quarterly 57 (5):456-469.
    Using Koszmider's strongly unbounded functions, we show the following consistency result: Suppose that κ, λ are infinite cardinals such that κ++ + ≤ λ, κ<κ = κ and 2κ = κ+, and η is an ordinal with κ+ ≤ η < κ++ and cf = κ+. Then, in some cardinal-preserving generic extension there is a superatomic Boolean algebra equation image such that equation image, equation image for every α < η and equation image. Especially, equation image and equation image can (...)
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  48. Zariski‐type topology for implication algebras.Manuel Abad, Diego Castaño & José P. Díaz Varela - 2010 - Mathematical Logic Quarterly 56 (3):299-309.
    In this work we provide a new topological representation for implication algebras in such a way that its one-point compactification is the topological space given in [1]. Some applications are given thereof.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  49. Super Special Codes using Super Matrices.W. B. Vasantha Kandasamy, Florentin Smarandache & K. Ilanthenral - 2010 - Stockholm, Sweden: Svenska fysikarkivet.
    The new classes of super special codes are constructed in this book using the specially constructed super special vector spaces. These codes mainly use the super matrices. These codes can be realized as a special type of concatenated codes.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  50. Fundamental results for pointfree convex geometry.Yoshihiro Maruyama - 2010 - Annals of Pure and Applied Logic 161 (12):1486-1501.
    Inspired by locale theory, we propose “pointfree convex geometry”. We introduce the notion of convexity algebra as a pointfree convexity space. There are two notions of a point for convexity algebra: one is a chain-prime meet-complete filter and the other is a maximal meet-complete filter. In this paper we show the following: the former notion of a point induces a dual equivalence between the category of “spatial” convexity algebras and the category of “sober” convexity spaces as well as a dual (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
1 — 50 / 176