Download or read book Rings Fields and Groups written by R. B. J. T. Allenby and published by Butterworth-Heinemann. This book was released on 1991 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an introduction to the results, methods and ideas which are now commonly studied in abstract algebra courses
Download or read book Hopf Algebras and Their Actions on Rings written by Susan Montgomery and published by American Mathematical Soc.. This book was released on 1993-10-28 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last ten years have seen a number of significant advances in Hopf algebras. The best known is the introduction of quantum groups, which are Hopf algebras that arose in mathematical physics and now have connections to many areas of mathematics. In addition, several conjectures of Kaplansky have been solved, the most striking of which is a kind of Lagrange's theorem for Hopf algebras. Work on actions of Hopf algebras has unified earlier results on group actions, actions of Lie algebras, and graded algebras. This book brings together many of these recent developments from the viewpoint of the algebraic structure of Hopf algebras and their actions and coactions. Quantum groups are treated as an important example, rather than as an end in themselves. The two introductory chapters review definitions and basic facts; otherwise, most of the material has not previously appeared in book form. Providing an accessible introduction to Hopf algebras, this book would make an excellent graduate textbook for a course in Hopf algebras or an introduction to quantum groups.
Download or read book Foundations of Applied Mathematics Volume I written by Jeffrey Humpherys and published by SIAM. This book was released on 2017-07-07 with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the essential foundations of both linear and nonlinear analysis necessary for understanding and working in twenty-first century applied and computational mathematics. In addition to the standard topics, this text includes several key concepts of modern applied mathematical analysis that should be, but are not typically, included in advanced undergraduate and beginning graduate mathematics curricula. This material is the introductory foundation upon which algorithm analysis, optimization, probability, statistics, differential equations, machine learning, and control theory are built. When used in concert with the free supplemental lab materials, this text teaches students both the theory and the computational practice of modern mathematical analysis. Foundations of Applied Mathematics, Volume 1: Mathematical Analysis includes several key topics not usually treated in courses at this level, such as uniform contraction mappings, the continuous linear extension theorem, Daniell?Lebesgue integration, resolvents, spectral resolution theory, and pseudospectra. Ideas are developed in a mathematically rigorous way and students are provided with powerful tools and beautiful ideas that yield a number of nice proofs, all of which contribute to a deep understanding of advanced analysis and linear algebra. Carefully thought out exercises and examples are built on each other to reinforce and retain concepts and ideas and to achieve greater depth. Associated lab materials are available that expose students to applications and numerical computation and reinforce the theoretical ideas taught in the text. The text and labs combine to make students technically proficient and to answer the age-old question, "When am I going to use this?
Download or read book Rings Fields and Vector Spaces written by Bharath Sethuraman and published by Springer Science & Business Media. This book was released on 1996-11-26 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using the proof of the non-trisectability of an arbitrary angle as a final goal, the author develops in an easy conversational style the basics of rings, fields, and vector spaces. Originally developed as a text for an introduction to algebra course for future high-school teachers at California State University, Northridge, the focus of this book is on exposition. It would serve extremely well as a focused, one-semester introduction to abstract algebra.
Download or read book Linear Algebra over Commutative Rings written by Bernard R. McDonald and published by CRC Press. This book was released on 2020-11-26 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph arose from lectures at the University of Oklahoma on topics related to linear algebra over commutative rings. It provides an introduction of matrix theory over commutative rings. The monograph discusses the structure theory of a projective module.
Download or read book The Algebraic Structure of Group Rings written by Donald S. Passman and published by Courier Corporation. This book was released on 2011-01-01 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: "'Highly recommended' by the Bulletin of the London Mathematical Society, this book offers a comprehensive, self-contained treatment of group rings. The subject involves the intersection of two essentially different disciplines, group theory and ring theory. The Bulletin of the American Mathematical Society hailed this treatment as 'a majestic account,' proclaiming it "encyclopedic and lucid." 1985 edition"--
Download or read book Separable Algebras over Commutative Rings written by Frank De Meyer and published by Springer. This book was released on 2006-11-15 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes were prepared by the authors for use in graduate courses and seminars, based on the work of many earlier mathematicians. In addition to very elementary results, presented for the convenience of the reader, Chapter I contains the Morita theorems and the definition of the projective class group of a commutative ring. Chapter II addresses the Brauer group of a commutative ring, and automorphisms of separable algebras. Chapter III surveys the principal theorems of the Galois theory for commutative rings. In Chapter IV the authors present a direct derivation of the first six terms of the seven-term exact sequence for Galois cohomology. In the fifth and final chapter the authors illustrate the preceding material with applications to the structure of central simple algebras and the Brauer group of a Dedekind domain, and they pose problems for further investigation. Exercises are included at the end of each chapter.
Download or read book Integers Polynomials and Rings written by Ronald S. Irving and published by Springer Science & Business Media. This book was released on 2004-01-08 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book began life as a set of notes that I developed for a course at the University of Washington entitled Introduction to Modern Algebra for Tea- ers. Originally conceived as a text for future secondary-school mathematics teachers, it has developed into a book that could serve well as a text in an - dergraduatecourseinabstractalgebraoracoursedesignedasanintroduction to higher mathematics. This book di?ers from many undergraduate algebra texts in fundamental ways; the reasons lie in the book’s origin and the goals I set for the course. The course is a two-quarter sequence required of students intending to f- ?ll the requirements of the teacher preparation option for our B.A. degree in mathematics, or of the teacher preparation minor. It is required as well of those intending to matriculate in our university’s Master’s in Teaching p- gram for secondary mathematics teachers. This is the principal course they take involving abstraction and proof, and they come to it with perhaps as little background as a year of calculus and a quarter of linear algebra. The mathematical ability of the students varies widely, as does their level of ma- ematical interest.
Download or read book Introduction to Abstract Algebra written by Benjamin Fine and published by JHU Press. This book was released on 2014-07-01 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approach to abstract algebra that eases student anxieties by building on fundamentals. Introduction to Abstract Algebra presents a breakthrough approach to teaching one of math's most intimidating concepts. Avoiding the pitfalls common in the standard textbooks, Benjamin Fine, Anthony M. Gaglione, and Gerhard Rosenberger set a pace that allows beginner-level students to follow the progression from familiar topics such as rings, numbers, and groups to more difficult concepts. Classroom tested and revised until students achieved consistent, positive results, this textbook is designed to keep students focused as they learn complex topics. Fine, Gaglione, and Rosenberger's clear explanations prevent students from getting lost as they move deeper and deeper into areas such as abelian groups, fields, and Galois theory. This textbook will help bring about the day when abstract algebra no longer creates intense anxiety but instead challenges students to fully grasp the meaning and power of the approach. Topics covered include: • Rings • Integral domains • The fundamental theorem of arithmetic • Fields • Groups • Lagrange's theorem • Isomorphism theorems for groups • Fundamental theorem of finite abelian groups • The simplicity of An for n5 • Sylow theorems • The Jordan-Hölder theorem • Ring isomorphism theorems • Euclidean domains • Principal ideal domains • The fundamental theorem of algebra • Vector spaces • Algebras • Field extensions: algebraic and transcendental • The fundamental theorem of Galois theory • The insolvability of the quintic
Download or read book Algebras Rings and Modules written by Michiel Hazewinkel and published by CRC Press. This book was released on 2016-04-05 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth centu
Download or read book A First Course in Abstract Algebra written by Marlow Anderson and published by CRC Press. This book was released on 2005-01-27 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most abstract algebra texts begin with groups, then proceed to rings and fields. While groups are the logically simplest of the structures, the motivation for studying groups can be somewhat lost on students approaching abstract algebra for the first time. To engage and motivate them, starting with something students know and abstracting from there
Download or read book Algebra II Ring Theory written by Carl Faith and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Exercises in Modules and Rings written by T.Y. Lam and published by Springer Science & Business Media. This book was released on 2009-12-08 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a compendium of exercises of varying degree of difficulty in the theory of modules and rings. It is the companion volume to GTM 189. All exercises are solved in full detail. Each section begins with an introduction giving the general background and the theoretical basis for the problems that follow.
Download or read book Algebra in Action written by Shahriar Shahriari and published by . This book was released on 2017 with total page 675 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text—based on the author's popular courses at Pomona College—provides a readable, student-friendly, and somewhat sophisticated introduction to abstract algebra. It is aimed at sophomore or junior undergraduates who are seeing the material for the first time. In addition to the usual definitions and theorems, there is ample discussion to help students build intuition and learn how to think about the abstract concepts. The book has over 1300 exercises and mini-projects of varying degrees of difficulty, and, to facilitate active learning and self-study, hints and short answers for many of the problems are provided. There are full solutions to over 100 problems in order to augment the text and to model the writing of solutions. Lattice diagrams are used throughout to visually demonstrate results and proof techniques. The book covers groups, rings, and fields. In group theory, group actions are the unifying theme and are introduced early. Ring theory is motivated by what is needed for solving Diophantine equations, and, in field theory, Galois theory and the solvability of polynomials take center stage. In each area, the text goes deep enough to demonstrate the power of abstract thinking and to convince the reader that the subject is full of unexpected results.
Download or read book Rings and Things and a Fine Array of Twentieth Century Associative Algebra written by Carl Clifton Faith and published by American Mathematical Soc.. This book was released on 2004 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys more than 125 years of aspects of associative algebras, especially ring and module theory. It is the first to probe so extensively such a wealth of historical development. Moreover, the author brings the reader up to date, in particular through his report on the subject in the second half of the twentieth century. Included in the book are certain categorical properties from theorems of Frobenius and Stickelberger on the primary decomposition of finite Abelian formulations of the latter by Krull, Goldman, and others; Maschke's theorem on the representation theory of finite groups over a field; and the fundamental theorems of Wedderburn on the structure of finite dimensional algebras Goldie, and others. A special feature of the book is the in-depth study of rings with chain condition on annihilator ideals pioneered by Noether, Artin, and Jacobson and refined and extended by many later mathematicians. Two of the author's prior works, Algebra: Rings, Modules and Categories, I and II (Springer-Verlag, 1973), are devoted to the development of modern associative algebra and ring and module theory. Those bibliography of over 1,600 references and is exhaustively indexed. In addition to the mathematical survey, the author gives candid and descriptive impressions of the last half of the twentieth century in ''Part II: Snapshots of fellow graduate students at the University of Kentucky and at Purdue, Faith discusses his Fulbright-Nato Postdoctoral at Heidelberg and at the Institute for Advanced Study (IAS) at Princeton, his year as a visiting scholar at Berkeley, and the many acquaintances he met there and in subsequent travels in India, Europe, and most recently, Barcelona. Comments on the first edition: ''Researchers in algebra should find it both full references as to the origin and development of the theorem ... I know of no other work in print which does this as thoroughly and as broadly.'' --John O'Neill, University of Detroit at Mercy '' 'Part II: Snapshots of Mathematicians of my age and younger will relish reading 'Snapshots'.'' --James A. Huckaba, University of Missouri-Columbia
Download or read book Rings Groups and Algebras written by X. Cao and published by CRC Press. This book was released on 1996-07-23 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Integrates and summarizes the most significant developments made by Chinese mathematicians in rings, groups, and algebras since the 1950s. Presents both survey articles and recent research results. Examines important topics in Hopf algebra, representation theory, semigroups, finite groups, homology algebra, module theory, valuation theory, and more."
Download or read book Abstract Algebra with Applications written by Karlheinz Spindler and published by CRC Press. This book was released on 1993-10-18 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.
