This book presents the foundations of a general theory of algebras. Often called “universal algebra”, this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is replete with useful illustrations and exercises that solidify the reader's understanding. The book begins by developing the main concepts and working tools of algebras and lattices, and continues with examples of classical algebraic systems like groups, semigroups, monoids, and categories. The essence of the book lies (...) in Chapter 4, which provides not only basic concepts and results of general algebra, but also the perspectives and intuitions shared by practitioners of the field. The book finishes with a study of possible uniqueness of factorizations of an algebra into a direct product of directly indecomposable algebras. There is enough material in this text for a two semester course sequence, but a one semester course could also focus primarily on Chapter 4, with additional topics selected from throughout the text. (shrink)

Consumer involvement in clinical research is an essential component of a comprehensive response during emergent health challenges. During the COVID-19 pandemic, the moderation of research policies and regulation to facilitate research may raise ethical issues. Meaningful, diverse consumer involvement can help to identify practical approaches to prioritize, design, and conduct rapidly developed clinical research amid current events. Consumer involvement might also elucidate the acceptability of flexible ethics review approaches that aim to protect participants whilst being sensitive to the challenging context (...) in which research is taking place. This article describes the main ethical challenges arising from pandemic research and how involving consumers and the community could enable resolution of such issues. (shrink)

Let be a finite collection of finite algebras of finite signature such that SP( ) has meet semi-distributive congruence lattices. We prove that there exists a finite collection 1 of finite algebras of the same signature, , such that SP( 1) is finitely axiomatizable.We show also that if , then SP( 1) is finitely axiomatizable. We offer new proofs of two important finite basis theorems of D. Pigozzi and R. Willard. Our actual results are somewhat more general than this abstract (...) indicates. (shrink)

Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}$$ \end{document} be a finite collection of finite algebras of finite signature such that SP(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}$$ \end{document}) has meet semi-distributive congruence lattices. We prove that there exists a finite collection \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}$$ \end{document}1 of finite algebras of the same signature, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}_1 \supseteq (...) \mathcal{K}$$ \end{document}, such that SP(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}$$ \end{document}1) is finitely axiomatizable.We show also that if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$HS(\mathcal{K}) \subseteq SP(\mathcal{K})$$ \end{document}, then SP(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}$$ \end{document}1) is finitely axiomatizable. We offer new proofs of two important finite basis theorems of D. Pigozzi and R. Willard. Our actual results are somewhat more general than this abstract indicates. (shrink)

We determine precisely those locally finite varieties of unary algebras of finite type which, when augmented by a ternary discriminator, generate a variety with a decidable theory.

The least element 0 of a finite meet semi-distributive lattice is a meet of meet-prime elements. We investigate conditions under which the least element of an algebraic, meet semi-distributive lattice is a (complete) meet of meet-prime elements. For example, this is true if the lattice has only countably many compact elements, or if |L| < 2ℵ0, or if L is in the variety generated by a finite meet semi-distributive lattice. We give an example of an algebraic, meet semi-distributive lattice that (...) has no meet-prime element or join-prime element. This lattice L has |L| = |LC| = 2ℵ0 where Lc is the set of compact elements of L. (shrink)

During evolution, the genomes of eukaryotic cells have undergone major restructuring to meet the new regulatory challenges associated with compartmentalization of the genetic material in the nucleus and the organelles acquired by endosymbiosis (mitochondria and plastids). Restructuring involved the loss of dispensable or redundant genes and the massive translocation of genes from the ancestral organelles to the nucleus. Genomics and bioinformatic data suggest that the process of DNA transfer from organelles to the nucleus still continues, providing raw material for evolutionary (...) tinkering in the nuclear genome. Recent reconstruction of these events in the laboratory has provided a unique tool to observe genome evolution in real time and to study the molecular mechanisms by which plastid genes are converted into functional nuclear genes. Here, we summarize current knowledge about plastid‐to‐nuclear gene transfer in the context of genome evolution and discuss new insights gained from experiments that recapitulate endosymbiotic gene transfer in the laboratory. BioEssays 30:556–566, 2008. © 2008 Wiley Periodicals, Inc. (shrink)

Assume that all algebras are atomless. (1) $Spind(A x B) = Spind(A) \cup Spind(B)$ . (2) $(\prod_{i\inI}^{w} = {\omega} \cup \bigcup_{i\inI}$ $Spind(A_{i})$ . Now suppose that $\kappa$ and $\lambda$ are infinite cardinals, with $kappa$ uncountable and regular and with $\kappa \textless \lambda$ . (3) There is an atomless Boolean algebra A such that $\mathfrak{u}(A) = \kappa$ and $i(A) = \lambda$ . (4) If $\lambda$ is also regular, then there is an atomless Boolean algebra A such that $t(A) = \mathfrak{s}(A) = (...) \kappa$ and $\mathfrak{a}(A) = \lambda$ . All results are in ZFC, and answer some problems posed in Monk [01] and Monk [ $\infty$ ]. (shrink)

Bradd Hart, Matthew Valeriote, A Structure Theorem for Strongly Abelian Varieties with Few Models.Bradd Hart, Sergei Starchenko, Addendum to "A Structure Theorem for Strongly Abelian Varieties.".Bradd Hart, Sergei Starchenko, Matthew Valeriote, Vaught's Conjecture for Varieties.B. Hart, S. Starchenko, Superstable Quasi-Varieties.B. Hart, A. Pillay, S. Starchenko, Triviality, NDOP and Stable Varieties.

We exhibit a construction which produces for every Turing machine T with two halting states μ 0 and μ -1 , an algebra B(T) (finite and of finite type) with the property that the variety generated by B(T) is residually large if T halts in state μ -1 , while if T halts in state μ 0 then this variety is residually bounded by a finite cardinal.

The statistical properties of a single quantum object and an ensemble of independent such objects are considered in detail for two-level systems. Computer simulations of dynamic zero-point quantum fluctuations for a single quantum object are reported and compared with analytic solutions for the ensemble case.

This book examines "Taylorean social theory," its sources, main characteristics and impact. Charles Taylor's meta-narrative of secularization in the West, prominently contained in his major work A Secular Age (2007), has brought new insight on the social and cultural factors that intervened in such process, the role of human agency, and particularly on the contemporary conditions of belief in North America and Europe. This study discusses what Taylor's approach has brought to the scholarly debate on Western secularization, which has been (...) carried on mostly in sociological terms. McKenzie interprets Taylor's views in a way that offers an original social theory. Such interpretation is possible with the help of sociologist Margaret Archer's "morphogenetic theory" and by making the most of Taylor's particular understanding of the method of the social sciences and of his philosophical views on human beings, knowledge and modernity. After exploring the philosophical and sociological sources informing Taylorean social theory and proposing its basic concepts and hermeneutic guidelines, the author compares it with two widespread theories of secularization: the now waning "orthodox" account and that proposed by Rational Choice Theory scholars, particularly prevalent in the United States. In doing so, the book shows in which ways Taylorean social theory supersedes them, what new issues it brings into the scholarly discussion, and what difficulties might limit its future development. (shrink)

The study compares Canadian and U.S. marketing researchers' attitudes, perceptions and intentions related to several areas of ethical concern. A particular focus involves salience of norms common to marketing research codes of ethics (COEs) and familiarity of such codes to marketing research professionals. Researchers' attitudes towards today's ethical climate are identified and compared between the two countries. Relationships are examined between familiarity, ethical intention and salience. Results indicate that U.S. and Canadian marketing researchers have similar perceptions of the relative importance (...) of specific ethical norms, but worldwide COEs do not reflect these perceptions. Canadian marketing researchers report having a greater familiarity with their firms' adopted COEs, but this finding is moderated by the type of researcher. Among other findings, results indicate that familiarity influences ethical intention only for highly salient issues. (shrink)

While educational settings may be envisioned as safe spaces that facilitate learning, foster creativity, and promote healthy development for youth, research has found that this is not always true for Black girls. Their negative experiences within educational settings are both gendered and racialized, often communicating broader societal perceptions of Black girls that ultimately shape their identity development. Utilizing semi-structured interviews with adolescent Black girls, the current investigation explored Black girls' educational experiences, their meaning making of Black girlhood, and the role (...) of parents in their positive development. By centering Black girls' voices, this study illuminated how Black girls negotiate their multiple marginalized identities and how their identities are shaped by their home and school environments. Findings revealed that Black girls are aware of the difficulties in navigating educational settings for Black girls, but this awareness was coupled with parental support that promoted positive gendered racial identities for Black girls in middle school and high school. This investigation advanced current knowledge of Black girls' identity development and highlighted the protective role of parental socialization. Future research directions and implications are also discussed. (shrink)

In the history of Chinese and European philosophy, metaphysics has played an outstanding role: it is a theoretical framework which provides the basis for a philosophical understanding of the world and the self. A theory of the self is well integrated in a metaphysical understanding of the totality of nature as a dynamic process of continuous changes. According to this view, the purpose of existence can be conceived of as the development and realization of the full potential given to the (...) individual by its nature. In regard to human nature specifically, this idea of self-realization includes the development of all cognitive faculties as well as of the moral character. Metaphysics has, however, suffered a loss of importance in current debates, especially in ethics. As a result, we observe the emergence of such philosophical views as moral skepticism and even nihilism. The consequence of this tendency has been the renunciation of a claim to understanding and to providing a solid ground for ethics. Yet an intercultural dialogue can provide us with some hope as the consolidation of debates on crucial topics of our traditions might indeed serve as the basis for a more powerful philosophy in the future. (shrink)

Peter Abelard (1079–1142 ce) was the most wide‐ranging philosopher of the twelfth century. He quickly established himself as a leading teacher of logic in and near Paris shortly after 1100. After his affair with Heloise, and his subsequent castration, Abelard became a monk, but he returned to teaching in the Paris schools until 1140, when his work was condemned by a Church Council at Sens. His logical writings were based around discussion of the “Old Logic”: Porphyry's Isagoge, aristotle'S Categories and (...) On Interpretation and boethius'S textbook on topical inference. They comprise a freestanding Dialectica (“Logic”; probably c.1116), a set of commentaries (known as the Logica [Ingredientibus], c. 1119) and a later (c. 1125) commentary on the Isagoge (Logica Nostrorum Petititoni Sociorum or Glossulae). In a work Abelard called his Theologia, issued in three main versions (between 1120 and c.1134), he attempted a logical analysis of trinitarian relations and explored the philosophical problems surrounding God's claims to omnipotence and omniscience. The Collationes (“Debates,” also known as “Dialogue between a Christian, a Philosopher and a Jew”; probably c.1130) present a rational investigation into the nature of the highest good, in which the Christian and the Philosopher (who seems to be modeled on a philosopher of pagan antiquity) are remarkably in agreement. The unfinished Scito teipsum (“Know thyself,” also known as the “Ethics”; c.1138) analyses moral action. (shrink)

Les différentes institutions européennes sont nées pour résoudre les problèmes de la production du stade avancé du capitaliste ainsi que de son armature géopolitique. Plus qu’un régime d’accumulation, c’est d’abord une infrastructure – au sens marxiste vulgaire – qui permettait une production et une consommation industrielles en Europe et un commerce inégal avec le Sud. Mais que se passe-t-il si ce n’est même plus du capitalisme, mais un nouveau mode de production? Celui qui extrude hors de lui-même une infrastructure très (...) différente, à une échelle planétaire? La question se pose alors de savoir si les anciennes infrastructures institutionnelles de l’Europe peuvent être adaptées à cette nouvelle réalité économique et politique, celle d’un Stack informationnel caractéristique du capitalisme de plateformes. (shrink)

L’objet de la présente recherche est d’interroger les mérites de la théorie utilitariste relative aux faillites personnelles, qui est dominante dans la littérature juridique depuis que le courant Law and Economics a gagné en importance. Nous démontrons que l’argumentation utilitariste, qui est assignée aux doctrines de l’acquittement des dettes personnelles par les spécialistes de Law and Economics travaillant dans le domaine du droit des faillites, soulève des questions normatives de taille et créée des tensions quand il s’agit de décrire le (...) phénomène. Ces deux problèmes invitent les théoriciens à proposer des modèles alternatifs pour décrire les conditions dans lesquelles nos systèmes juridiques soulagent les dettes des individus qui ne sont pas en mesure de les honorer. Dans notre ouvrage à paraître, The Virtue of Bankruptcy, nous embrassons ce projet. Ici, nous proposons une étape préliminaire à ce projet plus ambitieux en démontrant que les théories utilitaristes sur lesquelles s’appuient les contributions les plus importantes de la littérature sur la question à ce jour sont perfectibles lorsqu’il s’agit de comprendre les raisons et les circonstances dans lesquelles il est possible d’offrir un nouveau départ à ceux qui n’ont pas respecté leurs obligations financières. (shrink)

Does the law act for or against «the people»? Who are «the people»? This collection of essays by philosophers, historians, legal scholars, and others examines these questions in historical perspective; in law and literature; in contemporary, advanced, and developing societies; and with respect to gender and economics. What «the law» does and ought to represent is viewed semiotically as a problem admitting of no definitive answer.

By a classical theorem of Harvey Friedman, every countable nonstandard model $\mathcal {M}$ of a sufficiently strong fragment of ZF has a proper rank-initial self-embedding j, i.e., j is a self-embedding of $\mathcal {M}$ such that $j[\mathcal {M}]\subsetneq \mathcal {M}$, and the ordinal rank of each member of $j[\mathcal {M}]$ is less than the ordinal rank of each element of $\mathcal {M}\setminus j[\mathcal {M}]$. Here, we investigate the larger family of proper initial-embeddings j of models $\mathcal {M}$ of fragments of (...) set theory, where the image of j is a transitive submodel of $\mathcal {M}$. Our results include the following three theorems. In what follows, $\mathrm {ZF}^-$ is $\mathrm {ZF}$ without the power set axiom; $\mathrm {WO}$ is the axiom stating that every set can be well-ordered; $\mathrm {WF}$ is the well-founded part of $\mathcal {M}$ ; and $\Pi ^1_\infty \text{-}\mathrm {DC}_\alpha $ is the full scheme of dependent choice of length $\alpha $.Theorem A.There is an $\omega $ -standard countable nonstandard model $\mathcal {M}$ of $\mathrm {ZF}^-+\mathrm {WO}$ that carries no initial self-embedding $j:\mathcal {M} \longrightarrow \mathcal {M}$ other than the identity embedding.Theorem B.Every countable $\omega $ -nonstandard model $\mathcal {M}$ of $\ \mathrm {ZF}$ is isomorphic to a transitive submodel of the hereditarily countable sets of its own constructible universe $L^{\mathcal {M}}$.Theorem C.The following three conditions are equivalent for a countable nonstandard model $\mathcal {M}$ of $\mathrm {ZF}^{-}+\mathrm {WO}+\forall \alpha \ \Pi ^1_\infty \text{-}\mathrm {DC}_\alpha $. There is a cardinal in $\mathcal {M}$ that is a strict upper bound for the cardinality of each member of $\mathrm {WF}$. $\mathrm {WF}$ satisfies the powerset axiom.For all $n \in \omega $ and for all $b \in M$, there exists a proper initial self-embedding $j: \mathcal {M} \longrightarrow \mathcal {M}$ such that $b \in \mathrm {rng}$ and $j[\mathcal {M}] \prec _n \mathcal {M}$. (shrink)

In a number of membrane-bound viruses, ion channels are formed by integral membrane proteins. These channel proteins include M2 from influenza A, NB from influenza B, and, possibly, Vpu from HIV-1. M2 is important in facilitating uncoating of the influenza A viral genome and is the target of amantadine, an anti-influenza drug. The biological roles of NB and Vpu are less certain. In all cases, the protein contains a single transmembrane α-helix close to its N-terminus. Channels can be formed by (...) homo-oligomerization of these proteins, yielding bundles of transmembrane helices that span the membrane and surround a central ion-permeable pore. Molecular modeling may be used to integrate and interpret available experimental data concerning the structure of such transmembrane pores. This has proved successful for the M2 channel domain, where two independently derived models are in agreement with one another, and with solid-state nuclear magnetic resonance (NMR) data. Simulations based on channel models may yield insights into possible ion conduction and selectivity mechanisms. BioEssays 20:992–1000, 1998. © 1998 John Wiley & Sons, Inc. (shrink)

One of the founders of existentialism, the eminent philosopher Karl Jaspers here presents for the general reader an introduction to philosophy. In doing so, he also offers a lucid summary of his own philosophical thought. In Jaspers’ view, the source of philosophy is to be found “in wonder, in doubt, in a sense of forsakenness,” and the philosophical quest is a process of continual change and self-discovery. In a new foreword to this edition, Richard M. Owsley provides a brief overview (...) of Jaspers’ life and achievement. “An eloquent expression of a great hope that philosophy may again become an activity really relevant not only to the perennial problems of life and death but to the unusual configurations of such problems in our time.”—Julian N. Hartt, _Yale Review_ “Original, sincere, cultivated, and stimulating.”—_Philosophy_. (shrink)

We are free to get our theories where we will. As Einstein said, the emergence of a theory is like an egg laid by a chicken, "auf einmal ist es da.1" In practice theories are usually derived as improvements on earlier theories, as better tools are refinements of earlier, cruder ones; and they are directed explanatorily not at the facts of their own construction but at independently specifiable facts which, left unexplained by earlier theories, have therefore refuted them. A new (...) theory should cogently and directly explain all that its predecessors explain and in addition those particular facts which they conspicuously do not explain. The ideal is to have the simplest possible premises explaining most precisely the widest possible range of problematical facts. · 1. Ronald W. Clark, Einstein: The Life and Times , p.173 n. Ralph W. Rader has written Tennyson's "Maud": The Biographical Genesis. Among his influential articles are "Literary Form in Factual Narrative: The Example of Boswell's Johnson" and "The Concept of Genre and Eighteenth-Century Studies." He is professor of English at the University of California at Berkeley. His contributions to Critical Inquiry are "Explaining Our Literary Understanding: A Response to Jay Schleusener and Stanley Fish" , "The Dramatic Monologue and Related Lyric Forms", and "The Literary Theoretical Contribution of Sheldon Sacks". (shrink)

Originally published: Ithaca, N.Y.: Cornell University Press, 1989. With new pref.