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1. Universal Algebra: Fundamentals and Selected Topics (Chapman & Hall Pure and Applied Mathematics) by Clifford Bergman
Product Description Starting with the most basic notions, Universal Algebra: Fundamentals and Selected Topics introduces all the key elements needed to read and understand current research in this field. Based on the author’s twosemester course, the text prepares students for research work by providing a solid grounding in the fundamental constructions and concepts of universal algebra and by introducing a variety of recent research topics. The first part of the book focuses on core components, including subalgebras, congruences, lattices, direct and subdirect products, isomorphism theorems, a clone of operations, terms, free algebras, Birkhoff’s theorem, and standard Maltsev conditions. The second part covers topics that demonstrate the power and breadth of the subject. The author discusses the consequences of Jónsson’s lemma, finitely and nonfinitely based algebras, definable principal congruences, and the work of Foster and Pixley on primal and quasiprimal algebras. He also includes a proof of Murskiĭ’s theorem on primal algebras and presents McKenzie’s characterization of directly representable varieties, which clearly shows the power of the universal algebraic toolbox. The last chapter covers the rudiments of tame congruence theory. Throughout the text, a series of examples illustrates concepts as they are introduced and helps students understand how universal algebra sheds light on topics they have already studied, such as Abelian groups and commutative rings. Suitable for newcomers to the field, the book also includes carefully selected exercises that reinforce the concepts and push students to a deeper understanding of the theorems and techniques.
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2. Universal Algebra (Mathematics and Its Applications) by P.M. Cohn
Product Description The present book was conceived as an introduction for the user of universal algebra, rather than a handbook for the specialist, but when the first edition appeared in 1965, there were practically no other books entir~ly devoted to the subject, whether introductory or specialized. Today the specialist in the field is well provided for, but there is still a demand for an introduction to the subject to suit the user, and this seemed to justify a reissue of the book. Naturally some changes have had to be made; in particular, I have corrected all errors that have been brought to my notice. Besides errors, some obscurities in the text have been removed and the references brought up to date. I should like to express my thanks to a number of correspondents for their help, in particular C. G. d'Ambly, W. Felscher, P. Goralcik, P. J. Higgins, H.J. Hoehnke, J. R. Isbell, A. H. Kruse, E. J. Peake, D. Suter, J. S. Wilson. But lowe a special debt to G. M. Bergman, who has provided me with extensive comments. particularly on Chapter VII and the supplementary chapters. I have also con sulted reviews of the first edition, as well as the Italian and Russian translations.
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3. An Invitation to General Algebra and Universal Constructions (Universitext) by George M. Bergman
Product Description Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in noncategorytheoretic terms, of many familiar and notsofamiliar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in categorytheoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.
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4. A Course in Universal Algebra (Graduate Texts in Mathematics) by S. Burris, H. P. Sankappanavar
Product Description Universal algebra has enjoyed a particularly explosive growth in the last twenty years, and a student entering the subject now will find a bewildering amount of material to digest. This text is not intended to be encyclopedic; rather, a few themes central to universal algebra have been developed sufficiently to bring the reader to the brink of current research. The choice of topics most certainly reflects the authors' interests. Chapter I contains a brief but substantial introduction to lattices, and to the close connection between complete lattices and closure operators. In particular, everything necessary for the subsequent study of congruence lattices is included. Chapter II develops the most general and fundamental notions of uni versal algebrathese include the results that apply to all types of algebras, such as the homomorphism and isomorphism theorems. Free algebras are discussed in great detailwe use them to derive the existence of simple algebras, the rules of equational logic, and the important Mal'cev conditions. We introduce the notion of classifying a variety by properties of (the lattices of) congruences on members of the variety. Also, the center of an algebra is defined and used to characterize modules (up to polynomial equivalence). In Chapter III we show how neatly two famous resultsthe refutation of Euler's conjecture on orthogonal Latin squares and Kleene's character ization of languages accepted by finite automatacan be presented using universal algebra. We predict that such "applied universal algebra" will become much more prominent.
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5. Universal Algebra by George Grätzer
Product Description Universal Algebra has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science. Each chapter is followed by an extensive list of exercises and problems. The "state of the art" account also includes new appendices (with contributions from B. Jónsson, R. Quackenbush, W. Taylor, and G. Wenzel) and a well selected additional bibliography of over 1250 papers and books which makes this an indispensable new edition for students, faculty, and workers in the field.
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6. A Treatise on Universal Algebra: With Applications, Vol. 1 (Classic Reprint) by Alfred North Whitehead
Product Description Symbolic Reasoning allied to ordinary A lgebra. The chief examples of such systems are Hamilton sQ uaternions, Grassmann sC alculus of Extension and Boole sS ymbolic Logic. Such algebras have an intrinsic value for separate detailed study; also they are worthy of a comparative study, for the sake of the light thereby thrown on the general theory of symbolic reasoning, and on algebraic symbolism in particular. The comparative study necessarily presupposes some previous separate study, comparison being impossible without knowledge. Accordingly after the general principles of the whole subject have been discussed in Book I. of this volume, the remaining books of the volume are devoted to the separate study of the Algebra of Symbolic Logic, and of Grassmann sC alculus of Extension, and of the ideas involved in them. The idea of a generalized conception of space has been made prominent, in the belief that the properties and operations involved in it can be made to form a uniform method of interpretation of the various algebras. Thus it is hoped in this work to exhibit the algebras both as systems of symbolism, and also as engines for the investigation of the possibilities of thought and reasoning connected with the abstract general idea of space. A natural mode of comparison.between the algebras is thus at once provided by the unity of the subjectmatters of their interpretation. The detailed comparison of their symbolic structures has been adjourned to the second volume, in which it is intended to deal with Quaternions, Matrices, and the general theory of Linear A lgebras. This comparative anatomy of the subject was originated by B. Peirce spaper on Linear Associative A lgebra, and has been carried forward by more recent investigations in Germany. Firat read before theN ational Academy of Soienoes in Washington, 1871, and repabliahed in the American Journal of M
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7. Universal Algebra and Applications in Theoretical Computer Science by Klaus Denecke, Shelly L. Wismath
Product Description Over the past 20 years, the emergence of clone theory, hyperequational theory, commutator theory and tame congruence theory has led to a growth of universal algebra both in richness and in applications, especially in computer science. Yet most of the classic books on the subject are long out of print and, to date, no other book has integrated these theories with the longestablished work that supports them.
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8. Unknown Quantity: A Real and Imaginary History of Algebra by John Derbyshire
Product Description For curious nonmathematicians and armchair algebra buffs, John Derbyshire discovers the story behind the formulae, roots, and radicals. As he did so masterfully in Prime Obsession, Derbyshire brings the evolution of mathematical thinking to dramatic life by focusing on the key historical players. Unknown Quantity begins in the time of Abraham and Isaac and moves from Abel?s proof to the higher levels of abstraction developed by Galois through modernday advances. Derbyshire explains how a simple turn of thought from ?this plus this equals this? to ?this plus what equals this?? gave birth to a whole new way of perceiving the world. With a historian?s narrative authority and a beloved teacher?s clarity and passion, Derbyshire leads readers on an intellectually satisfying and pleasantly challenging journey through the development of abstract mathematical thought.
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9. Universal Algebra Workbook for Collegiate, Freshman, Adults, and Teens by WorlWide Publishing
Product Description Algebra Workbook: For Kids, High School Kids, and College Bound Freshman. Helps understand vast and complex concepts. Derived from India, Algebra has revolutionized the world and the children in it. Algebra is a core function of society and society revolves around Algebra. Children and Adults alike need to understand Algebra. This book helps solve that problem.
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10. A Course in Universal Algebra (Graduate Texts in Mathematics) by S. Burris, H. P. Sankappanavar
Product Description Universal algebra has enjoyed a particularly explosive growth in the last twenty years, and a student entering the subject now will find a bewildering amount of material to digest. This text is not intended to be encyclopedic; rather, a few themes central to universal algebra have been developed sufficiently to bring the reader to the brink of current research. The choice of topics most certainly reflects the authors' interests. Chapter I contains a brief but substantial introduction to lattices, and to the close connection between complete lattices and closure operators. In particular, everything necessary for the subsequent study of congruence lattices is included. Chapter II develops the most general and fundamental notions of uni versal algebrathese include the results that apply to all types of algebras, such as the homomorphism and isomorphism theorems. Free algebras are discussed in great detailwe use them to derive the existence of simple algebras, the rules of equational logic, and the important Mal'cev conditions. We introduce the notion of classifying a variety by properties of (the lattices of) congruences on members of the variety. Also, the center of an algebra is defined and used to characterize modules (up to polynomial equivalence). In Chapter III we show how neatly two famous resultsthe refutation of Euler's conjecture on orthogonal Latin squares and Kleene's character ization of languages accepted by finite automatacan be presented using universal algebra. We predict that such "applied universal algebra" will become much more prominent.
... Read more 
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