Abstract Algebra: A Comprehensive Treatment, 1st Edition (Hardback) book cover

Abstract Algebra

A Comprehensive Treatment, 1st Edition

By Claudia Menini, Freddy Van Oystaeyen

CRC Press

776 pages

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Hardback: 9780824709853
pub: 2004-04-20
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pub: 2004-04-20
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Description

In one exceptional volume, Abstract Algebra covers subject matter typically taught over the course of two or three years and offers a self-contained presentation, detailed definitions, and excellent chapter-matched exercises to smooth the trajectory of learning algebra from zero to one. Field-tested through advance use in the ERASMUS educational project in Europe, this ambitious, comprehensive book includes an original treatment of representation of finite groups that avoids the use of semisimple ring theory and explains sets, maps, posets, lattices, and other essentials of the algebraic language; Peano's axioms and cardinality; groupoids, semigroups, monoids, groups; and normal subgroups.

Reviews

"This is a comprehensive book of over 750 pages, that covers the material of algebra courses in the first two or three years of a bachelor's degree program. …This a nice book is written in a very clear and explanatory style, offering a self-contained presentation and complete proofs, as well as well-chosen exercises, illustrative examples, and some interesting historical notes."

-Mathematical Reviews, Issue 2005e

"Many examples and worked exercises make the text easy to read. Written in a clear and detailed style it will be a valuable basis for students who want to learn algebra from the beginning."

-H. Mitsch, Wien, Monatshefte für Mathematik

"The experience of the authors together with a careful presentation of material makes this book a valuable addition to modern textbooks in algebra."

-EMS Newsletter, June 2005

Table of Contents

Sets

Maps

Cartesian Product and Binary Relations

Posets, Lattices, Zorn's Lemma

Peano's Axions

Cardinality

Quotient Sets

Groupoids, Semigroups, Monoids

Groups

The Integers

Congruences

Normal Subgroups

Isomorphism Theorems for Groups

Cyclic Groups

Direct Product of Groups

The Symmetric Group

Further Results on Groups

Rings, Ideals, and Homomorphisms

Quotient Rings

Direct Product of Rings

About the Series

Chapman & Hall/CRC Pure and Applied Mathematics

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT002000
MATHEMATICS / Algebra / General