Download or read book Commutative Ring Theory and Applications written by Marco Fontana and published by CRC Press. This book was released on 2017-07-27 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Featuring presentations from the Fourth International Conference on Commutative Algebra held in Fez, Morocco, this reference presents trends in the growing area of commutative algebra. With contributions from nearly 50 internationally renowned researchers, the book emphasizes innovative applications and connections to algebraic number theory, geome

Download or read book Advances in Ring Theory written by Sergio R. López-Permouth and published by Springer Science & Business Media. This book was released on 2011-01-28 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of refereed research and expository articles by both plenary and other speakers at the International Conference on Algebra and Applications held at Ohio University in June 2008, to honor S.K. Jain on his 70th birthday. The articles are on a wide variety of areas in classical ring theory and module theory, such as rings satisfying polynomial identities, rings of quotients, group rings, homological algebra, injectivity and its generalizations, etc. Included are also applications of ring theory to problems in coding theory and in linear algebra.

Download or read book Abstract Algebra written by Thomas Judson and published by Orthogonal Publishing L3c. This book was released on 2023-08-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.

Download or read book Ring Constructions and Applications written by Andrei V. Kelarev and published by World Scientific. This book was released on 2002 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the definitions of several ring constructions used in various applications. The concept of a groupoid-graded ring includes many of these constructions as special cases and makes it possible to unify the exposition. Recent research results on groupoid-graded rings and more specialized constructions are presented. In addition, there is a chapter containing open problems currently considered in the literature. Ring Constructions and Applications can serve as an excellent introduction for graduate students to many ring constructions as well as to essential basic concepts of group, semigroup and ring theories used in proofs. Contents: Preliminaries; Graded Rings; Examples of Ring Constructions; The Jacobson Radical; Groups of Units; Finiteness Conditions; PI-Rings and Varieties; Gradings of Matrix Rings; Examples of Applications; Open Problems. Readership: Graduate students and researchers using ring constructions in their work.

Download or read book Commutative Ring Theory written by Hideyuki Matsumura and published by Cambridge University Press. This book was released on 1989-05-25 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.

Download or read book Introduction to Modern Algebra and Its Applications written by Nadiya Gubareni and published by CRC Press. This book was released on 2021-06-23 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an introduction to modern abstract algebra and its applications. It covers all major topics of classical theory of numbers, groups, rings, fields and finite dimensional algebras. The book also provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. In particular, it considers algorithm RSA, secret sharing algorithms, Diffie-Hellman Scheme and ElGamal cryptosystem based on discrete logarithm problem. It also presents Buchberger’s algorithm which is one of the important algorithms for constructing Gröbner basis. Key Features: Covers all major topics of classical theory of modern abstract algebra such as groups, rings and fields and their applications. In addition it provides the introduction to the number theory, theory of finite fields, finite dimensional algebras and their applications. Provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. Presents numerous examples illustrating the theory and applications. It is also filled with a number of exercises of various difficulty. Describes in detail the construction of the Cayley-Dickson construction for finite dimensional algebras, in particular, algebras of quaternions and octonions and gives their applications in the number theory and computer graphics.

Download or read book Cox Rings written by Ivan Arzhantsev and published by Cambridge University Press. This book was released on 2015 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a largely self-contained introduction to Cox rings and their applications in algebraic and arithmetic geometry.

Download or read book Algebra Chapter 0 written by Paolo Aluffi and published by American Mathematical Soc.. This book was released on 2021-11-09 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.

Download or read book Advances in Algebra and Model Theory written by M Droste and published by CRC Press. This book was released on 1998-01-29 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains 25 surveys in algebra and model theory, all written by leading experts in the field. The surveys are based around talks given at conferences held in Essen, 1994, and Dresden, 1995. Each contribution is written in such a way as to highlight the ideas that were discussed at the conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community. The topics include field and ring theory as well as groups, ordered algebraic structure and their relationship to model theory. Several papers deal with infinite permutation groups, abelian groups, modules and their relatives and representations. Model theoretic aspects include quantifier elimination in skew fields, Hilbert's 17th problem, (aleph-0)-categorical structures and Boolean algebras. Moreover symmetry questions and automorphism groups of orders are covered. This work contains 25 surveys in algebra and model theory, each is written in such a way as to highlight the ideas that were discussed at Conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community.

Download or read book Further Algebra and Applications written by Paul M. Cohn and published by Springer Science & Business Media. This book was released on 2011-06-27 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is the second volume of a revised edition of P.M. Cohn's classic three-volume text Algebra, widely regarded as one of the most outstanding introductory algebra textbooks. Volume Two focuses on applications. The text is supported by worked examples, with full proofs, there are numerous exercises with occasional hints, and some historical remarks.

Download or read book Ring Theory and Its Applications written by Dinh Van Huynh and published by American Mathematical Soc.. This book was released on 2014-02-21 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Ring Theory Session in honor of T. Y. Lam's 70th birthday, at the 31st Ohio State-Denison Mathematics Conference, held from May 25-27, 2012, at The Ohio State University, Columbus, Ohio. Included are expository articles and research papers covering topics such as cyclically presented modules, Eggert's conjecture, the Mittag-Leffler conditions, clean rings, McCoy rings, QF rings, projective and injective modules, Baer modules, and Leavitt path algebras. Graduate students and researchers in many areas of algebra will find this volume valuable as the papers point out many directions for future work; in particular, several articles contain explicit lists of open questions.

Download or read book Advances in Ring Theory written by S.K. Jain and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Foundations of Module and Ring Theory written by Robert Wisbauer and published by Routledge. This book was released on 2018-05-11 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive introduction to module theory and the related part of ring theory, including original results as well as the most recent work. It is a useful and stimulating study for those new to the subject as well as for researchers and serves as a reference volume. Starting form a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. For a module M, the smallest Grothendieck category containing it is denoted by o[M] and module theory is developed in this category. Developing the techniques in o[M] is no more complicated than in full module categories and the higher generality yields significant advantages: for example, module theory may be developed for rings without units and also for non-associative rings. Numerous exercises are included in this volume to give further insight into the topics covered and to draw attention to related results in the literature.

Download or read book Semirings Algebraic Theory And Applications In Computer Science written by Hanns Joachim Weinert and published by World Scientific. This book was released on 1998-10-30 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the algebraic theory of semirings and, in this context, to basic algebraic concepts as e.g. semigroups, lattices and rings. It includes an algebraic theory of infinite sums as well as a detailed treatment of several applications in theoretical computer science. Complete proofs, various examples and exercises (some of them with solutions) make the book suitable for self-study. On the other hand, a more experienced reader who looks for information about the most common concepts and results on semirings will find cross-references throughout the book, a comprehensive bibliography and various hints to it.

Download or read book Hopf Algebras written by Jeffrey Bergen and published by CRC Press. This book was released on 2004-01-28 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume publishes key proceedings from the recent International Conference on Hopf Algebras held at DePaul University, Chicago, Illinois. With contributions from leading researchers in the field, this collection deals with current topics ranging from categories of infinitesimal Hopf modules and bimodules to the construction of a Hopf algebraic

Download or read book Cohen Macaulay Rings written by Winfried Bruns and published by Cambridge University Press. This book was released on 1998-06-18 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last two decades Cohen-Macaulay rings and modules have been central topics in commutative algebra. This book meets the need for a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of Cohen-Macaulay rings, Gorenstein rings, local cohomology, and canonical modules. A separate chapter is devoted to Hilbert functions (including Macaulay's theorem) and numerical invariants derived from them. The authors emphasize the study of explicit, specific rings, making the presentation as concrete as possible. So the general theory is applied to Stanley-Reisner rings, semigroup rings, determinantal rings, and rings of invariants. Their connections with combinatorics are highlighted, e.g. Stanley's upper bound theorem or Ehrhart's reciprocity law for rational polytopes. The final chapters are devoted to Hochster's theorem on big Cohen-Macaulay modules and its applications, including Peskine-Szpiro's intersection theorem, the Evans-Griffith syzygy theorem, bounds for Bass numbers, and tight closure. Throughout each chapter the authors have supplied many examples and exercises which, combined with the expository style, will make the book very useful for graduate courses in algebra. As the only modern, broad account of the subject it will be essential reading for researchers in commutative algebra.

Download or read book Paraconsistency written by Walter Alexandr Carnielli and published by CRC Press. This book was released on 2002-04-10 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a study on the foundations of a large class of paraconsistent logics from the point of view of the logics of formal inconsistency. It also presents several systems of non-standard logics with paraconsistent features.