Algebra : Groups, Rings, and Fields - Louis Rowen

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Algebra

Name: Algebra
Brand: A K PETERS LTD (MA)
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Groups, Rings, and Fields

By: Louis Rowen

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Hardcover | 10 January 1995 | Edition Number 1

At a Glance

Hardcover
264 Pages

Dimensions(cm)
24.13 x 16.51 x 2.54

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This text presents the concepts of higher algebra in a comprehensive and modern way for self-study and as a basis for a high-level undergraduate course. The author is one of the preeminent researchers in this field and brings the reader up to the recent frontiers of research including never-before-published material. From the table of contents: - Groups: Monoids and Groups - Cauchyis Theorem - Normal Subgroups - Classifying Groups - Finite Abelian Groups - Generators and Relations - When Is a Group a Group? (Cayley's Theorem) - Sylow Subgroups - Solvable Groups - Rings and Polynomials: An Introduction to Rings - The Structure Theory of Rings - The Field of Fractions - Polynomials and Euclidean Domains - Principal Ideal Domains - Famous Results from Number Theory - I Fields: Field Extensions - Finite Fields - The Galois Correspondence - Applications of the Galois Correspondence - Solving Equations by Radicals - Transcendental Numbers: e and p - Skew Field Theory - Each chapter includes a set of exercises

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Non-Fiction Mathematics Algebra Groups & Group Theory

Preface
Table of Principal Notation
Prerequisites
Groups	p. 1
Monoids and Groups	p. 2
How to Divide: Lagrange's Theorem, Cosets, and an Application to Number Theory	p. 8
Cauchy's Theorem: How to Show a Number Is Greater Than 1	p. 15
Introduction to the Classification of Groups: Homomorphisms, Isomorphisms, and Invariants	p. 23
Normal Subgroups - The Building Blocks of the Structure Theory	p. 29
Classifying Groups - Cyclic Groups and Direct Products	p. 39
Finite Abelian Groups	p. 46
Generators and Relations	p. 56
When Is a Group a Group? (Cayley's Theorem)	p. 66
Recounting: Conjugacy Classes and the Class Formula	p. 72
Sylow Subgroups: A New Invariant	p. 79
Solvable Groups: What Could Be Simpler?	p. 86
Rings and Polynomials	p. 97
An Introduction to Rings	p. 98
The Structure Theory of Rings	p. 103
The Field of Fractions - A Study in Generalization	p. 109
Polynomials and Euclidean Domains	p. 114
Principal Ideal Domains: Induction without Numbers	p. 124
Roots of Polynomials	p. 133
(Optional) Applications: Famous Results from Number Theory	p. 138
Irreducible Polynomials	p. 146
Fields	p. 155
Field Extensions: Creating Roots of Polynomials	p. 159
The Problems of Antiquity	p. 167
Adjoining Roots to Polynomials: Splitting Fields	p. 175
Finite Fields	p. 187
The Galois Correspondence	p. 191
Applications of the Galois Correspondence	p. 200
Solving Equations by Radicals	p. 207
Appendix A. Transcendental Numbers: e and [pi]	p. 219
Appendix B. Skew Field Theory	p. 224
Index	p. 233
Table of Contents provided by Blackwell. All Rights Reserved.

Algebra

Groups, Rings, and Fields

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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