1st Edition

Abstract Algebra A Comprehensive Treatment

    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.

    Cartesian Product and Binary Relations
    Posets, Lattices, Zorn's Lemma
    Peano's Axions
    Quotient Sets
    Groupoids, Semigroups, Monoids
    The Integers
    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


    CLAUDIA MENINI  University of Ferrara , Ferrera, Italy . FREDDY VAN OYSTAEYEN  University of Antwerp, UIA, Antwerp, Belgium.

    "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