
Author 
Pierre Antoine Grillet 
ISBN10 
9780387715681 
Year 
20070721 
Pages 
674 
Language 
en 
Publisher 
Springer Science & Business Media 
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A completely reworked new edition of this superb textbook. This key work is geared to the needs of the graduate student. It covers, with proofs, the usual major branches of groups, rings, fields, and modules. Its inclusive approach means that all of the necessary areas are explored, while the level of detail is ideal for the intended readership. The text tries to promote the conceptual understanding of algebra as a whole, doing so with a masterful grasp of methodology. Despite the abstract subject matter, the author includes a careful selection of important examples, together with a detailed elaboration of the more sophisticated, abstract theories.

Author 
Israel Kleiner 
ISBN10 
9780817646851 
Year 
20070920 
Pages 
168 
Language 
en 
Publisher 
Springer Science & Business Media 
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This book does nothing less than provide an account of the intellectual lineage of abstract algebra. The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared insoluble by classical means. A major theme of the book is to show how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved. Mathematics instructors, algebraists, and historians of science will find the work a valuable reference.

Author 
P. B. Bhattacharya 
ISBN10 
0521466296 
Year 
19941125 
Pages 
487 
Language 
en 
Publisher 
Cambridge University Press 
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This is a selfcontained text on abstract algebra for senior undergraduate and senior graduate students, which gives complete and comprehensive coverage of the topics usually taught at this level. The book is divided into five parts. The first part contains fundamental information such as an informal introduction to sets, number systems, matrices, and determinants. The second part deals with groups. The third part treats rings and modules. The fourth part is concerned with field theory. Much of the material in parts II, III, and IV forms the core syllabus of a course in abstract algebra. The fifth part goes on to treat some additional topics not usually taught at the undergraduate level, such as the WedderburnArtin theorem for semisimple artinian rings, NoetherLasker theorem, the SmithNormal form over a PID, finitely generated modules over a PID and their applications to rational and Jordan canonical forms and the tensor products of modules. Throughout, complete proofs have been given for all theorems without glossing over significant details or leaving important theorems as exercises. In addition, the book contains many examples fully worked out and a variety of problems for practice and challenge. Solution to the oddnumbered problems are provided at the end of the book to encourage the student in problem solving. This new edition contains an introduction to categories and functors, a new chapter on tensor products and a discussion of the new (1993) approach to the celebrated NoetherLasker theorem. In addition, there are over 150 new problems and examples.
Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some indepth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings. The emphasis throughout has been to motivate the introduction and development of important algebraic concepts using as many examples as possible.

Author 
Allan Clark 
ISBN10 
0486647250 
Year 
1984 
Pages 
205 
Language 
en 
Publisher 
Courier Corporation 
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Lucid coverage of the major theories of abstract algebra, with helpful illustrations and exercises included throughout. Unabridged, corrected republication of the work originally published 1971. Bibliography. Index. Includes 24 tables and figures.

Author 
Paul B. Garrett 
ISBN10 
9781584886891 
Year 
20070925 
Pages 
472 
Language 
en 
Publisher 
CRC Press 
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Designed for an advanced undergraduate or graduatelevel course, Abstract Algebra provides an exampleoriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroomtested, howto manual takes a more narrative approach than the stiff formalism of many other textbooks, presenting coherent storylines to convey crucial ideas in a studentfriendly, accessible manner. An unusual feature of the text is the systematic characterization of objects by universal mapping properties, rather than by constructions whose technical details are irrelevant. Addresses Common Curricular Weaknesses In addition to standard introductory material on the subject, such as Lagrange's and Sylow's theorems in group theory, the text provides important specific illustrations of general theory, discussing in detail finite fields, cyclotomic polynomials, and cyclotomic fields. The book also focuses on broader background, including brief but representative discussions of naive set theory and equivalents of the axiom of choice, quadratic reciprocity, Dirichlet's theorem on primes in arithmetic progressions, and some basic complex analysis. Numerous worked examples and exercises throughout facilitate a thorough understanding of the material.

Author 
Rudolf Lidl 
ISBN10 
9781475729412 
Year 
20130314 
Pages 
488 
Language 
en 
Publisher 
Springer Science & Business Media 
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Accessible to junior and senior undergraduate students, this survey contains many examples, solved exercises, sets of problems, and parts of abstract algebra of use in many other areas of discrete mathematics. Although this is a mathematics book, the authors have made great efforts to address the needs of users employing the techniques discussed. Fully worked out computational examples are backed by more than 500 exercises throughout the 40 sections. This new edition includes a new chapter on cryptology, and an enlarged chapter on applications of groups, while an extensive chapter has been added to survey other applications not included in the first edition. The book assumes knowledge of the material covered in a course on linear algebra and, preferably, a first course in (abstract) algebra covering the basics of groups, rings, and fields.

Author 
Charles C Pinter 
ISBN10 
9780486474175 
Year 
20100114 
Pages 
384 
Language 
en 
Publisher 
Courier Corporation 
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Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easytoread treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.

Author 
I. H. Sheth 
ISBN10 
8120317378 
Year 
20040801 
Pages 
348 
Language 
en 
Publisher 
PHI Learning Pvt. Ltd. 
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Author 
W. Keith Nicholson 
ISBN10 
9781118135358 
Year 
20120320 
Pages 
535 
Language 
en 
Publisher 
John Wiley & Sons 
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Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."—Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text. The Fourth Edition features important concepts as well as specialized topics, including: The treatment of nilpotent groups, including the Frattini and Fitting subgroups Symmetric polynomials The proof of the fundamental theorem of algebra using symmetric polynomials The proof of Wedderburn's theorem on finite division rings The proof of the WedderburnArtin theorem Throughout the book, worked examples and realworld problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises. Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upperundergraduate and beginninggraduate levels. The book also serves as a valuable reference and selfstudy tool for practitioners in the fields of engineering, computer science, and applied mathematics.

Author 
Dan Saracino 
ISBN10 
9781478610137 
Year 
20080902 
Pages 
313 
Language 
en 
Publisher 
Waveland Press 
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The Second Edition of this classic text maintains the clear exposition, logical organization, and accessible breadth of coverage that have been its hallmarks. It plunges directly into algebraic structures and incorporates an unusually large number of examples to clarify abstract concepts as they arise. Proofs of theorems do more than just prove the stated results; Saracino examines them so readers gain a better impression of where the proofs come from and why they proceed as they do. Most of the exercises range from easy to moderately difficult and ask for understanding of ideas rather than flashes of insight. The new edition introduces five new sections on field extensions and Galois theory, increasing its versatility by making it appropriate for a twosemester as well as a onesemester course.

Author 
Ronald Solomon 
ISBN10 
0821847953 
Year 
2003 
Pages 
227 
Language 
en 
Publisher 
American Mathematical Soc. 
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This undergraduate text takes a novel approach to the standard introductory material on groups, rings, and fields. At the heart of the text is a semihistorical journey through the early decades of the subject as it emerged in the revolutionary work of Euler, Lagrange, Gauss, and Galois. Avoiding excessive abstraction whenever possible, the text focuses on the central problem of studying the solutions of polynomial equations. Highlights include a proof of the Fundamental Theorem of Algebra, essentially due to Euler, and a proof of the constructability of the regular 17gon, in the manner of Gauss. Another novel feature is the introduction of groups through a meditation on the meaning of congruence in the work of Euclid. Everywhere in the text, the goal is to make clear the links connecting abstract algebra to Euclidean geometry, high school algebra, and trigonometry, in the hope that students pursuing a career as secondary mathematics educators will carry away a deeper and richer understanding of the high school mathematics curriculum. Another goal is to encourage students, insofar as possible in a textbook format, to build the course for themselves, with exercises integrally embedded in the text of each chapter.

Author 
Gertrude Ehrlich 
ISBN10 
9780486291864 
Year 
20130513 
Pages 
352 
Language 
en 
Publisher 
Courier Corporation 
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A text in abstract algebra for undergraduate mathematics majors, this volume contains enough material for a twosemester course. It presents extensive coverage of set theory, groups, rings, modules, vector spaces, and fields. Examples, definitions, theorems, and proofs appear throughout, along with numerous practice exercises at the end of each section. 1991 edition.

Author 
Clive Reis 
ISBN10 
9789814730563 
Year 
20160830 
Pages 
576 
Language 
en 
Publisher 
World Scientific Publishing Co Inc 
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This second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata. This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya–Burnside Enumeration, Mutually Orthogonal Latin Squares, ErrorCorrecting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems. Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced — via congruence classes — to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless. In this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible. Request Inspection Copy

Author 
DIPAK CHATTERJEE 
ISBN10 
8120328701 
Year 
20050101 
Pages 
372 
Language 
en 
Publisher 
PHI Learning Pvt. Ltd. 
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Appropriate for undergraduate courses, this second edition has a new chapter on lattice theory, many revisions, new solved problems and additional exercises in the chapters on group theory, boolean algebra and matrix theory. The text offers a systematic, wellplanned, and elegant treatment of the main themes in abstract algebra. It begins with the fundamentals of set theory, basic algebraic structures such as groups and rings, and special classes of rings and domains, and then progresses to extension theory, vector space theory and finally the matrix theory. The boolean algebra by virtue of its relation to abstract algebra also finds a proper place in the development of the text. The students develop an understanding of all the essential results such as the Cayley's theorem, the Lagrange's theorem, and the Isomorphism theorem, in a rigorous and precise manner. Sufficient numbers of examples have been worked out in each chapter so that the students can grasp the concepts, the ideas, and the results of structure of algebraic objects in a comprehensive way. The chapterend exercises are designed to enhance the student's ability to further explore and interconnect various essential notions.