Abstract Algebra

Contents
Preface
About the Authors
1. Groups
	1.1 Semigroups and groups
	1.2 Subgroups and cosets
	1.3 Normal subgroups and quotient groups
	1.4 Homomorphisms and isomorphisms
	1.5 Cyclic groups
	1.6 Symmetric groups and alternating groups
	1.7 Group extensions and Jordan–Hölder theorem
	1.8 Solvable and nilpotent groups
	1.9 Group actions
	1.10 Sylow theorems
	1.11 Summary of the chapter
2. Rings
	2.1 The definition of a ring and fundamental properties
	2.2 Ideals and quotient rings
	2.3 Quaternions
	2.4 Homomorphisms of rings
	2.5 Factorizations in a domain
	2.6 Prime ideals and maximal ideals
	2.7 Principal ideal domains and Euclidean domains
	2.8 Polynomials over a ring
	2.9 Polynomial rings over a domain
	2.10 Symmetric polynomials
	2.11 Summary of the chapter
3. Modules
	3.1 Fundamental concepts
	3.2 Matrices over a ring and the endomorphism rings of modules
	3.3 Free modules
	3.4 Finitely generated modules over a principal ideal domain
	3.5 Finitely generated abelian groups
	3.6 Canonical forms of linear transformations
	3.7 Summary of the chapter
4. Fields
	4.1 Field extensions
	4.2 Algebraic extensions
	4.3 Straightedge and compass construction
	4.4 Splitting fields
	4.5 Galois groups
	4.6 Galois extensions and Galois correspondence
	4.7 Finite fields
	4.8 Separable polynomials and perfect fields
	4.9 Separable extensions
	4.10 The inverse Galois problem
	4.11 Abelian extensions
	4.12 Solvability by radicals
	4.13 Summary of the chapter
Bibliography
Index