Search results for 'Commutative rings Congresses' (try it on Scholar)

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  1.  2
    Lawrence P. Belluce & Antonio Di Nola (2009). Commutative Rings Whose Ideals Form an MV‐Algebra. Mathematical Logic Quarterly 55 (5):468-486.
    In this work we introduce a class of commutative rings whose defining condition is that its lattice of ideals, augmented with the ideal product, the semi-ring of ideals, is isomorphic to an MV-algebra. This class of rings coincides with the class of commutative rings which are direct sums of local Artinian chain rings with unit.
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  2. John N. Crossley (ed.) (1975). Algebra and Logic: Papers From the 1974 Summer Research Institute of the Australian Mathematical Society, Monash University, Australia. Springer-Verlag.
     
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  3.  16
    Mihai Prunescu (2003). Diophantine Properties of Finite Commutative Rings. Archive for Mathematical Logic 42 (3):293-302.
    Simple observations on diophantine definability over finite commutative rings lead to a characterization of those rings in terms of their diophantine behavior.
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  4. Gena Puninski & Carlo Toffalori (2009). Towards the Decidability of the Theory of Modules Over Finite Commutative Rings. Annals of Pure and Applied Logic 159 (1):49-70.
    On the basis of the Klingler–Levy classification of finitely generated modules over commutative noetherian rings we approach the old problem of classifying finite commutative rings R with a decidable theory of modules. We prove that if R is wild, then the theory of all R-modules is undecidable, and verify decidability of this theory for some classes of tame finite commutative rings.
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  5.  9
    Misao Nagayama (1992). On Boolean Algebras and Integrally Closed Commutative Regular Rings. Journal of Symbolic Logic 57 (4):1305-1318.
    In this paper we consider properties, related to model-completeness, of the theory of integrally closed commutative regular rings. We obtain the main theorem claiming that in a Boolean algebra B, the truth of a prenex Σn-formula whose parameters ai partition B, can be determined by finitely many conditions built from the first entry of Tarski invariant T(ai)'s, n-characteristic D(n, ai)'s and the quantities S(ai, l) and S'(ai, l) for $l < n$. Then we derive two important theorems. One (...)
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  6.  9
    Luis F. Caceres-Duque (2003). Ideal Theories of Some Commutative Rings. Bulletin of the Section of Logic 32 (1/2):9-18.
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  7.  5
    G. L. Cherlin (1973). Algebraically Closed Commutative Rings. Journal of Symbolic Logic 38 (3):493-499.
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  8. Gregory L. Cherlin & Joachim Reineke (1976). Categoricity and Stability of Commutative Rings. Annals of Mathematical Logic 9 (4):367-399.
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  9. Stephen D. Comer (1983). Review: G. L. Cherlin, The Model-Companion of a Class of Structures; L. Lipshitz, D. Saracino, The Model Companion of the Theory of Commutative Rings Without Nilpotent Elements; Angus Macintyre, Model-Completeness for Sheaves of Structures. [REVIEW] Journal of Symbolic Logic 48 (2):496-496.
     
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  10.  2
    Dan Saracino (1999). Prime E.C. Commutative Rings in Characteristic N ≥. Journal of Symbolic Logic 64 (2):629-633.
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  11. J. C. C. McKinsey (1944). Review: Alfred L. Foster, B. A. Bernstein, Symmetric Approach to Commutative Rings, With Duality Theorem: Boolean Duality as a Special Case. [REVIEW] Journal of Symbolic Logic 9 (4):97-97.
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  12.  4
    Kay Smith (1984). Commutative Regular Rings and Boolean-Valued Fields. Journal of Symbolic Logic 49 (1):281-297.
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  13. L. van den Dries (1977). Artin-Schreier Theory for Commutative Regular Rings. Annals of Mathematical Logic 12 (2):113-150.
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  14.  6
    K.-P. Podewski & Joachim Reineke (1979). Algebraically Closed Commutative Local Rings. Journal of Symbolic Logic 44 (1):89-94.
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  15.  9
    Bruce I. Rose (1978). Rings Which Admit Elimination of Quantifiers. Journal of Symbolic Logic 43 (1):92-112.
    We say that a ring admits elimination of quantifiers, if in the language of rings, {0, 1, +, ·}, the complete theory of R admits elimination of quantifiers. Theorem 1. Let D be a division ring. Then D admits elimination of quantifiers if and only if D is an algebraically closed or finite field. A ring is prime if it satisfies the sentence: ∀ x ∀ y ∃ z (x = 0 ∨ y = 0 ∨ xzy ≠ 0). (...)
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  16.  9
    Olivier Finkel & Stevo Todorčević (2012). A Hierarchy of Tree-Automatic Structures. Journal of Symbolic Logic 77 (1):350-368.
    We consider ω n -automatic structures which are relational structures whose domain and relations are accepted by automata reading ordinal words of length ω n for some integer n ≥ 1. We show that all these structures are ω-tree-automatic structures presentable by Muller or Rabin tree automata. We prove that the isomorphism relation for ω 2 -automatic (resp. ω n -automatic for n > 2) boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, (...)
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  17.  3
    Gérard Leloup (1994). Rings of Monoids Elementarily Equivalent to Polynomial Rings. Annals of Pure and Applied Logic 68 (2):173-180.
    Let l be a commutative field; Bauval [1] showed that the theory of the ring l[X1,...,Xm] is the same as the weak second-order theory of the field l. Now, l[X1,...,Xm] is the ring of the monoid m, so it may be asked what properties of m we can deduce from the theory of l[;m], that is, if l[m] is elementarily equivalent to the ring of monoid k[G], with k, a field and G, a monoid, what do we know not (...)
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  18.  20
    Michael Rings (2013). Doing It Their Way: Rock Covers, Genre, and Appreciation. Journal of Aesthetics and Art Criticism 71 (1):55-63.
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  19.  10
    Hanspeter Rings (1987). Das strukturalistische Problem der theoretischen Begriffe und seine Lösung. Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 18 (1-2):296-312.
    In especially the Sneed-Stegmüller structuralist theory a so-called problem of theoretical terms emerges. But this problem bases on a questionable presupposition . And the structuralist solution of this problem, the so-called Ramsey-Sneed-solution, is also problematic , , ). Beyond this the structuralist assertion is problematic, that the problem of theoretical terms and his Ramsey-Sneed-solution is empirically relevant . On the basis of the discussed systematic and empirical defects of the problem of theoretical terms and its solution, the so-called non-statement view₂, (...)
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  20.  1
    Eduardo J. Dubuc (2012). Representation Theory of MV-Algebras (Vol 161, Pg 1024, 2010). Annals of Pure and Applied Logic 163 (9):1358 - 1358.
    In this paper we develop a general representation theory for MV-algebras. We furnish the appropriate categorical background to study this problem. Our guide line is the theory of classifying topoi of coherent extensions of universal algebra theories. Our main result corresponds, in the case of MV-algebras and MV-chains, to the representation of commutative rings with unit as rings of global sections of sheaves of local rings. We prove that any MV-algebra is isomorphic to the MV-algebra of (...)
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  21.  2
    Teresa Bigorajska (1995). On Σ1‐Definable Functions Provably Total in I ∏ 1−. Mathematical Logic Quarterly 41 (1):135-137.
    We prove the following theorem: Let φ be a formula in the language of the theory PA− of discretely ordered commutative rings with unit of the form ∃yφ′ with φ′ and let ∈ Δ0 and let fφ: ℕ → ℕ such that fφ = y iff φ′ & < xK). Here I ∏math image1− denotes the theory PA− plus the scheme of induction for formulas φ of the form ∀yφ′ with φ′ ∈ Δ0.
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  22.  9
    Bernhard Banaschewski (1994). A New Proof That “Krull Implies Zorn”. Mathematical Logic Quarterly 40 (4):478-480.
    In the present note we give a direct deduction of the Axiom of Choice from the Maximal Ideal Theorem for commutative rings with unit.
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  23.  1
    Henri Lombardi (2006). Structures Algébriques Dynamiques, Espaces Topologiques Sans Points Et Programme de Hilbert. Annals of Pure and Applied Logic 137 (1):256-290.
    A possible relevant meaning of Hilbert’s program is the following one: “give a constructive semantic for classical mathematics”. More precisely, give a systematic interpretation of classical abstract proofs about abstract objects, as constructive proofs about constructive versions of these objects.If this program is fulfilled we are able “at the end of the tale” to extract constructive proofs of concrete results from classical abstract proofs of these results.Dynamical algebraic structures or geometric theories seem to be a good tool for doing this (...)
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  24. Norihiro Kamide (2009). Temporal Non-Commutative Logic: Expressing Time, Resource, Order and Hierarchy. Logic and Logical Philosophy 18 (2):97-126.
    A first-order temporal non-commutative logic TN[l], which has no structural rules and has some l-bounded linear-time temporal operators, is introduced as a Gentzen-type sequent calculus. The logic TN[l] allows us to provide not only time-dependent, resource-sensitive, ordered, but also hierarchical reasoning. Decidability, cut-elimination and completeness (w.r.t. phase semantics) theorems are shown for TN[l]. An advantage of TN[l] is its decidability, because the standard first-order linear-time temporal logic is undecidable. A correspondence theorem between TN[l] and a resource (...)
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  25.  64
    Thomas Mormann, Squares of Oppositions, Commutative Diagrams, and Galois Connections for Topological Spaces and Similarity Structures.
    The aim of this paper is to elucidate the relationship between Aristotelian conceptual oppositions, commutative diagrams of relational structures, and Galois connections.This is done by investigating in detail some examples of Aristotelian conceptual oppositions arising from topological spaces and similarity structures. The main technical device for this endeavor is the notion of Galois connections of order structures.
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  26. Hans Schoutens (1999). Existentially Closed Models of the Theory of Artinian Local Rings. Journal of Symbolic Logic 64 (2):825-845.
    The class of all Artinian local rings of length at most l is ∀ 2 -elementary, axiomatised by a finite set of axioms Art l . We show that its existentially closed models are Gorenstein, of length exactly l and their residue fields are algebraically closed, and, conversely, every existentially closed model is of this form. The theory Got l of all Artinian local Gorenstein rings of length l with algebraically closed residue field is model complete and the (...)
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  27.  86
    Kinjalk Lochan, Seema Satin & Tejinder P. Singh (2012). Statistical Thermodynamics for a Non-Commutative Special Relativity: Emergence of a Generalized Quantum Dynamics. [REVIEW] Foundations of Physics 42 (12):1556-1572.
    There ought to exist a description of quantum field theory which does not depend on an external classical time. To achieve this goal, in a recent paper we have proposed a non-commutative special relativity in which space-time and matter degrees of freedom are treated as classical matrices with arbitrary commutation relations, and a space-time line element is defined using a trace. In the present paper, following the theory of Trace Dynamics, we construct a statistical thermodynamics for the non- (...) special relativity, and show that one arrives at a generalized quantum dynamics in which space and time are non-classical and have an operator status. In a future work, we will show how standard quantum theory on a classical space-time background is recovered from here. (shrink)
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  28.  9
    Denis R. Hirschfeldt, Bakhadyr Khoussainov, Richard A. Shore & Arkadii M. Slinko (2002). Degree Spectra and Computable Dimensions in Algebraic Structures. Annals of Pure and Applied Logic 115 (1-3):71-113.
    Whenever a structure with a particularly interesting computability-theoretic property is found, it is natural to ask whether similar examples can be found within well-known classes of algebraic structures, such as groups, rings, lattices, and so forth. One way to give positive answers to this question is to adapt the original proof to the new setting. However, this can be an unnecessary duplication of effort, and lacks generality. Another method is to code the original structure into a structure in the (...)
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  29.  40
    Gerd Niestegge (2009). A Representation of Quantum Measurement in Nonassociative Algebras. Foundations of Physics 39 (2):120-136.
    Starting from an abstract setting for the Lüders-von Neumann quantum measurement process and its interpretation as a probability conditionalization rule in a non-Boolean event structure, the author derived a certain generalization of operator algebras in a preceding paper. This is an order-unit space with some specific properties. It becomes a Jordan operator algebra under a certain set of additional conditions, but does not own a multiplication operation in the most general case. A major objective of the present paper is the (...)
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  30.  4
    Oleg V. Belegradek (1994). The Model Theory of Unitriangular Groups. Annals of Pure and Applied Logic 68 (3):225-261.
    he model theory of groups of unitriangular matrices over rings is studied. An important tool in these studies is a new notion of a quasiunitriangular group. The models of the theory of all unitriangular groups are algebraically characterized; it turns out that all they are quasiunitriangular groups. It is proved that if R and S are domains or commutative associative rings then two quasiunitriangular groups over R and S are isomorphic only if R and S are isomorphic (...)
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  31.  18
    S. Twareque Ali, Claudio Carmeli, Teiko Heinosaari & Alessandro Toigo (2009). Commutative POVMs and Fuzzy Observables. Foundations of Physics 39 (6):593-612.
    In this paper we review some properties of fuzzy observables, mainly as realized by commutative positive operator valued measures. In this context we discuss two representation theorems for commutative positive operator valued measures in terms of projection valued measures and describe, in some detail, the general notion of fuzzification. We also make some related observations on joint measurements.
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  32.  13
    Rostislav Horčík (2012). Minimal Varieties of Representable Commutative Residuated Lattices. Studia Logica 100 (6):1063-1078.
    We solve several open problems on the cardinality of atoms in the subvariety lattice of residuated lattices and FL-algebras [4, Problems 17—19, pp. 437]. Namely, we prove that the subvariety lattice of residuated lattices contains continuum many 4-potent commutative representable atoms. Analogous results apply also to atoms in the subvariety lattice of FL i -algebras and FL o -algebras. On the other hand, we show that the subvariety lattice of residuated lattices contains only five 3-potent commutative representable atoms (...)
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  33.  6
    María E. Alonso, Henri Lombardi & Hervé Perdry (2008). Elementary Constructive Theory of Henselian Local Rings. Mathematical Logic Quarterly 54 (3):253-271.
    We give an elementary theory of Henselian local rings and construct the Henselisation of a local ring. All our theorems have an algorithmic content.
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  34.  6
    Lee Cronk & Bria Dunham (2007). Amounts Spent on Engagement Rings Reflect Aspects of Male and Female Mate Quality. Human Nature 18 (4):329-333.
    Previous research has shown that the qualities of nuptial gifts among nonhumans and marriage-related property transfers in human societies such as bridewealth and dowry covary with aspects of mate quality. This article explores this issue for another type of marriage-related property transfer: engagement rings. We obtained data on engagement ring costs and other variables through a mail survey sent to recently married individuals living in the American Midwest. This article focuses on survey responses regarding rings that were purchased (...)
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  35.  2
    L. Yu Glebsky, E. I. Gordon & C. Ward Hensen (2007). On Finite Approximations of Topological Algebraic Systems. Journal of Symbolic Logic 72 (1):1 - 25.
    We introduce and discuss a concept of approximation of a topological algebraic system A by finite algebraic systems from a given class K. If A is discrete, this concept agrees with the familiar notion of a local embedding of A in a class K of algebraic systems. One characterization of this concept states that A is locally embedded in K iff it is a subsystem of an ultraproduct of systems from K. In this paper we obtain a similar characterization of (...)
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  36.  15
    Norihiro Kamide (2010). Dynamic Non-Commutative Logic. Journal of Logic, Language and Information 19 (1):33-51.
    A first-order dynamic non-commutative logic (DN), which has no structural rules and has some program operators, is introduced as a Gentzen-type sequent calculus. Decidability, cut-elimination and completeness theorems are shown for DN or its fragments. DN is intended to represent not only program-based, resource-sensitive, ordered, sequence-based, but also hierarchical (tree-based) reasoning.
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  37.  3
    Claude Sureson (2009). Model Companion and Model Completion of Theories of Rings. Archive for Mathematical Logic 48 (5):403-420.
    Extending the language of rings to include predicates for Jacobson radical relations, we show that the theory of regular rings defined by Carson, Lipshitz and Saracino is the model completion of the theory of semisimple rings. Removing the requirement on the Jacobson radical (reduced to {0}), we prove that the theory of rings with no nilpotents does not admit a model companion relative to this augmented language.
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  38.  1
    Jānis Cīrulis (2015). On Some Classes of Commutative Weak BCK-Algebras. Studia Logica 103 (3):479-490.
    Formally, a description of weak BCK-algebras can be obtained by replacing the first BCK axiom \ - \le z - y}\) by its weakening \. It is known that every weak BCK-algebra is completely determined by the structure of its initial segments. We consider weak BCK-algebras with De Morgan complemented, orthocomplemented and orthomodular sections, as well as those where sections satisfy a certain compatibility condition, and characterize each of these classes of algebras by an equation or quasi-equation. For instance, those (...)
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  39.  1
    Hervé Perdry (2008). Lazy Bases: A Minimalist Constructive Theory of Noetherian Rings. Mathematical Logic Quarterly 54 (1):70-82.
    We give a constructive treatment of the theory of Noetherian rings. We avoid the usual restriction to coherent rings; we can even deal with non-discrete rings. We introduce the concept of rings with certifiable equality which covers discrete rings and much more. A ring R with certifiable equality can be fitted with a partial ideal membership test for ideals of R. Lazy bases of ideals of R [X ] are introduced in order to derive a (...)
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  40.  12
    D. J. Hurley & M. A. Vandyck (2014). A Minimal Framework for Non-Commutative Quantum Mechanics. Foundations of Physics 44 (11):1168-1187.
    Deformation quantisation is applied to ordinary Quantum Mechanics by introducing the star product in a configuration space combining a Riemannian structure with a Poisson one. A Hilbert space compatible with such a configuration space is designed. The dynamics is expressed by a Hermitian Hamiltonian containing a scalar potential and a one-form potential. As a simple illustration, it is shown how a particular type of non-commutativity of the star product is interpretable as generating the Zeeman effect of ordinary Quantum Mechanics.
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  41. Norihiro Kamide & Motohiko Mouri (2007). Natural Deduction Systems for Some Non-Commutative Logics. Logic and Logical Philosophy 16 (2-3):105-146.
    Varieties of natural deduction systems are introduced for Wansing’s paraconsistent non-commutative substructural logic, called a constructive sequential propositional logic (COSPL), and its fragments. Normalization, strong normalization and Church-Rosser theorems are proved for these systems. These results include some new results on full Lambek logic (FL) and its fragments, because FL is a fragment of COSPL.
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  42. Gennadi Puninski (1999). Cantor-Bendixson Rank of the Ziegler Spectrum Over a Commutative Valuation Domain. Journal of Symbolic Logic 64 (4):1512-1518.
    We calculate the Cantor-Bendixson rank of the Ziegler spectrum over a commutative valuation domain R proving that it is equal to the double Krull dimension of R.
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  43. Bruce I. Rose (1978). The ℵ1-Categoricity of Strictly Upper Triangular Matrix Rings Over Algebraically Closed Fields. Journal of Symbolic Logic 43 (2):250 - 259.
    Let n ≥ 3. The following theorems are proved. Theorem. The theory of the class of strictly upper triangular n × n matrix rings over fields is finitely axiomatizable. Theorem. If R is a strictly upper triangular n × n matrix ring over a field K, then there is a recursive map σ from sentences in the language of rings with constants for K into sentences in the language of rings with constants for R such that $K (...)
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  44.  2
    Raf Cluckers, Jamshid Derakhshan, Eva Leenknegt & Angus Macintyre (2013). Uniformly Defining Valuation Rings in Henselian Valued Fields with Finite or Pseudo-Finite Residue Fields. Annals of Pure and Applied Logic 164 (12):1236-1246.
    We give a definition, in the ring language, of Zp inside Qp and of Fp[[t]] inside Fp), which works uniformly for all p and all finite field extensions of these fields, and in many other Henselian valued fields as well. The formula can be taken existential-universal in the ring language, and in fact existential in a modification of the language of Macintyre. Furthermore, we show the negative result that in the language of rings there does not exist a uniform (...)
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  45.  4
    Brian Bocking (2013). Flagging Up Buddhism: Charles Pfoundes (Omoie Tetzunostzuke) Among the International Congresses and Expositions, 1893–1905. Contemporary Buddhism 14 (1):17-37.
    Charles James William Pfoundes (1840?1907), a young emigrant from Southeast Ireland, spent most of his adult life in Japan, received a Japanese name ?Omoie Tetzunostzuke?, first embraced and then turned against Theosophy and, from 1893, was ordained in several Japanese Buddhist traditions. Lacking independent means but educated, intellectually curious, entrepreneurial, fluent in Japanese and with a keen interest in Asian culture, Pfoundes subsisted as a cultural intermediary, explaining Japan and Asia to both Japanese and foreign audiences and actively seeking involvement (...)
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  46.  16
    V. Michele Abrusci & Paul Ruet (1999). Non-Commutative Logic I: The Multiplicative Fragment. Annals of Pure and Applied Logic 101 (1):29-64.
    We introduce proof nets and sequent calculus for the multiplicative fragment of non-commutative logic, which is an extension of both linear logic and cyclic linear logic. The two main technical novelties are a third switching position for the non-commutative disjunction, and the structure of order variety.
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  47.  29
    Maciej Kandulski (1995). On Commutative and Nonassociative Syntactic Calculi and Categorial Grammars. Mathematical Logic Quarterly 41 (2):217-235.
    Two axiomatizations of the nonassociative and commutative Lambek syntactic calculus are given and their equivalence is proved. The first axiomatization employs Permutation as the only structural rule, the second one, with no Permutation rule, employs only unidirectional types. It is also shown that in the case of the Ajdukiewicz calculus an analogous equivalence is valid only in the case of a restricted set of formulas. Unidirectional axiomatizations are employed in order to establish the generative power of categorial grammars based (...)
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  48.  11
    Enrico Marchioni (2012). Amalgamation Through Quantifier Elimination for Varieties of Commutative Residuated Lattices. Archive for Mathematical Logic 51 (1-2):15-34.
    This work presents a model-theoretic approach to the study of the amalgamation property for varieties of semilinear commutative residuated lattices. It is well-known that if a first-order theory T enjoys quantifier elimination in some language L, the class of models of the set of its universal consequences ${\rm T_\forall}$ has the amalgamation property. Let ${{\rm Th}(\mathbb{K})}$ be the theory of an elementary subclass ${\mathbb{K}}$ of the linearly ordered members of a variety ${\mathbb{V}}$ of semilinear commutative residuated lattices. We (...)
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  49.  10
    Jan Krajíček & Thomas Scanlon (2000). Combinatorics with Definable Sets: Euler Characteristics and Grothendieck Rings. Bulletin of Symbolic Logic 6 (3):311-330.
    We recall the notions of weak and strong Euler characteristics on a first order structure and make explicit the notion of a Grothendieck ring of a structure. We define partially ordered Euler characteristic and Grothendieck ring and give a characterization of structures that have non-trivial partially ordered Grothendieck ring. We give a generalization of counting functions to locally finite structures, and use the construction to show that the Grothendieck ring of the complex numbers contains as a subring the ring of (...)
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  50.  5
    Krzysztof Krupiński (2011). On Relationships Between Algebraic Properties of Groups and Rings in Some Model-Theoretic Contexts. Journal of Symbolic Logic 76 (4):1403-1417.
    We study relationships between certain algebraic properties of groups and rings definable in a first order structure or *-closed in a compact G-space. As a consequence, we obtain a few structural results about ω-categorical rings as well as about small, nm-stable compact G-rings, and we also obtain surprising relationships between some conjectures concerning small profinite groups.
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