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A first course in abstract algebra

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Contents:

I GROUPS AND SUBGROUPS
1 Introduction and examples
2 Binary operations
3 Isomorphic binary structure
4 Groups
5 Subgroups
6 Cyclic groups
7 Generating sets and cayley digraphs

II PERMUTATIONS, COSETS, AND DIRECT PRODUCTS
8 Group of permutations
9 Orbits, cycles and the alternating groups
10 Cosets and the theorem of lagrange
11 Direct products and finitely generated abelian group
12 Plane isometries

III HOMOMORPHISMS AND FAAACTOR GROUPS
13 Homomorphisms
14 Factor group
15 Factor-group computations and simple groups
16 Group action on a set
17 Application of G-sets to counting

IV RINGS AND FIELDS
18 Rings and fields
19 Integral domains
20 Fermat’s and euler’s theorems
21 he field of quotients of an integral domain
22 Rings pf polynomials
23 Factorization of polynomials over a field
24 Noncommutative examples
25 Ordered rings and ideals

V IDEALS AND FACTOR RINGS
26 Homomorphisms and factor rings
27 Prime and maximal ideals
28 Grobner bases for ideals

VI EXTENSION FIELDS
29 Introduction to extension fields
30 Vector spaces
31 Algebraic extensions
32 Geometric constructions
33 Finite fields

VII ADVANCED GROUP THEORY
34 Isomorphisms theorems
35 Series of groups
36 Sylow theorems
37 Applications of the sylow theory
38 Free abelian groups
39 Free groups
40 Group presentations

VIII GROUPS IN TOPOLOGY
41 Simplicial complexes and homology groups
42 Computations of homology groups
43 More homology computations and applications
44 Homological algebra

IX FACTORIZATION
45 Unique factorization domains
46 Euclidean domains
47 Gaussian integers and multiplicative norms

X AUTOMORPHISMS AND GALOIS THEORY
48 Automorphisms of fields
49 The isomorphisms extension theorem
50 Splitting fields
51 Separable extensions
52 Totally inseparable extensions
53 Galois theory
54 Illustrations of galois theory
55 Cyclotomic extensions
56 Insolvability of the quintic

Appendix: matrix algebra
Index

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Availability

Detail Information

Series Title

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Call Number

512 FRA a

Publisher

Boston : Addison-Wesley., 2003

Collation

xii, 519 hal.; ilus.; 24 cm

Language

English

ISBN/ISSN

0201763907

Classification

512

Content Type

-

Media Type

-

Carrier Type

-

Edition

Seventh edition

Subject(s)

Algebra, Abstract
Aljabar abstrak

Specific Detail Info

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Statement of Responsibility

John B. Fraleigh

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