عنوان

A first course in abstract algebra /

(Number (ISBN

0201763907

(Number (ISBN

0321156080

(Number (ISBN

9780201763904

(Number (ISBN

9780321156082

Number

b533752

Title Proper

A first course in abstract algebra /

General Material Designation

[Book]

First Statement of Responsibility

John B. Fraleigh ; historical notes by Victor Katz

Edition Statement

Seventh edition

Place of Publication, Distribution, etc.

Boston :

Name of Publisher, Distributor, etc.

Addison-Wesley,

Date of Publication, Distribution, etc.

[2003]

Date of Publication, Distribution, etc.

©2003

Specific Material Designation and Extent of Item

xii, 520 pages :

Other Physical Details

illustrations ;

Dimensions

24 cm

Text of Note

Includes bibliographical references (pages 483-485) and index

Text of Note

Sets and relations -- I. Groups and subgroups. Introduction and examples -- Binary operations -- Isomorphic binary structures -- Groups -- Subgroups -- Cyclic groups -- Generating sets and Cayley digraphs -- II. Permutations, cosets, and direct products. Groups of permutations -- Orbits, cycles, and the alternating groups -- Cosets and the theorem of Lagrange -- Direct products and finitely generated Abelian groups -- Plane isometries -- III. Homomorphisms and factor groups. Homomorphisms -- Factor groups -- Factor-group computations and simple groups -- Group action on a set -- Applications of G-sets to counting -- IV. Rings and fields. Rings and fields -- Integral domains -- Fermat's and Euler's theorems -- The field of quotients of an integral domain -- Rings of polynomials -- Factorization of polynomials over a field -- Noncommutative examples -- Ordered rings and fields -- V. Ideals and factor rings. Homomorphisms and factor rings -- Prime and maximal ideas -- Gröbner bases for ideals -- VI. Extension fields. Introduction to extension fields -- Vector spaces -- Algebraic extensions -- Geometric constructions -- Finite fields -- VII. Advanced group theory. Isomorphism theorems -- Series of groups -- Sylow theorems -- Applications of the Sylow theory -- Free Abelian groups -- Free groups -- Group presentations -- VIII. Groups in topology. Simplicial complexes and homology groups -- Computations of homology groups -- More homology computations and applications -- Homological algebra -- IX. Factorization. Unique factorization domains -- Euclidean domains -- Gaussian integers and multiplicative norms -- X. Automorphisms and Galois theory. Automorphisms of fields -- The isomorphism extension theorem -- Splitting fields -- Separable extensions -- Totally inseparable extensions -- Galois theory -- Illustrations of Galois theory -- Cyclotomic extensions -- Insolvability of the quintic -- Appendix: Matrix algebra

0

Text of Note

This is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, it should give students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. Features include: a classical approach to abstract algebra focussing on applications; an accessible pedagogy including historical notes written by Victor Katz; and a study of group theory

Source for Acquisition/Subscription Address

TVG

Stock Number

66429

Algebra, Abstract

Fraleigh, John B

Katz, Victor J

Cataloguing Rules (Descriptive Conventions))

rda

Electronic name

[Book]

Y