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Abstract Algebra : The Basic Graduate Year

By Ash, Robert B.

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Book Id: WPLBN0000695483
Format Type: PDF eBook
File Size: 110.57 KB
Reproduction Date: 2005

Title: Abstract Algebra : The Basic Graduate Year  
Author: Ash, Robert B.
Language: English
Subject: Science., Mathematics, Logic
Publication Date:


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Ash, R. B. (n.d.). Abstract Algebra : The Basic Graduate Year. Retrieved from

Mathematics document containing theorems and formulas.

Table of Contents
TABLE OF CONTENTS CHAPTER 0 PREREQUISITES 0.1 Elementary Number Theory 0.2 Set Theory 0.3 Linear Algebra CHAPTER 1 GROUP FUNDAMENTALS 1.1 Groups and Subgroups 1.2 Permutation Groups 1.3 Cosets, Normal Subgroups and Homomorphisms 1.4 The Isomorphism Theorems 1.5 Direct Products CHAPTER 2 RING FUNDAMENTALS 2.1 Basic Definitions and Properties 2.2 Ideals, Homomorphisms and Quotient Rings 2.3 The Isomorphism Theorems For Rings 2.4 Maximal and Prime Ideals 2.5 Polynomial Rings 2.6 Unique Factorization 2.7 Principal Ideal Domains and Euclidean Domains 2.8 Rings of Fractions 2.9 Irreducible Polynomials CHAPTER 3 FIELD FUNDAMENTALS 3.1 Field Extensions 3.2 Splitting Fields 3.3 Algebraic Closures 3.4 Separability 3.5 Normal Extensions CHAPTER 4 MODULE FUNDAMENTALS 4.1 Modules and Algebras 4.2 The Isomorphism Theorems For Modules 4.3 Direct Sums and Free Modules 4.4 Homomorphisms and Matrices 4.5 Smith Normal Form 4.6 Fundamental Structure Theorems 4.7 Exact Sequences and Diagram Chasing CHAPTER 5 SOME BASIC TECHNIQUES OF GROUP THEORY 5.1 Groups Acting on Sets 5.2 The Orbit-Stabilizer Theorem 5.3 Applications to Combinatorics 5.4 The Sylow Theorems 5.5 Applications of the Sylow Theorems 5.6 Composition Series 5.7 Solvable and Nilpotent Groups5.8 Generators and Relations CHAPTER 6 GALOIS THEORY 6.1 Fixed Fields and Galois Groups 6.2 The Fundamental Theorem 6.3 Computing a Galois Group Directly 6.4 Finite Fields 6.5 Cyclotomic Fields 6.6 The Galois Group of a Cubic 6.7 Cyclic and Kummer Extensions 6.8 Solvability by Radicals 6.9 Transcendental Extensions Appendix to Chapter 6


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