Universities Press

Algebra: A Graduate Course

I. Martin Isaacs

ISBN: 9780821852149 | Year: 2010 | Paperback | Pages: 528 | Language : English

Book Size: 158 x 240 mm | Territorial Rights: Restricted| Series Indian Editions of AMS Titles

Price: 1845.00

About the Book

This book, contains more than enough material for a two-semester graduate-level abstract algebra course, including groups, rings and modules, fields and Galois theory, an introduction to algebraic number theory, and the rudiments of algebraic geometry. This book could be used for self study as well as for a course text, and so full details of almost all proofs are included. There are hundreds of problems, many being far from trivial.

Contributors (Author(s), Editor(s), Translator(s), Illustrator(s) etc.)

I. Martin Isaacs, University of Wisconsin, Madison, Wisconsin, USA

Table of Content

Part One: Non Commutative Algebra: Definitions and Examples of Groups; Subgroups and Cosets; Homomorphisms; Group Actions; The Sylow Theorems and p-groups; Permutation Groups; New Groups from Old; Solvable and Nilpotent Groups; Transfer; Operator Groups and Unique Decompositions; Module Theory without Rings; Rings, Ideals, and Modules; Simple Modules and Primitive Rings; Artinian Rings and Projective Modules; An Introduction to Character Theory
Part Two: Commutative Algebra: Polynomial Rings, PIDs, and UFDs; Field Extensions; Galosis Theory; Separability and Inseparability; Cyclotomy and Geometric Constructions; Finite Fields; Roots, Radicals, and Real Numbers; Norms, Traces, and Discriminants; Transcendental Extensions; The Artin-Schreier Theorem; Ideal Theory; Noetherian Rings; Integrality; Dedekind Domains; Algebraic Sets and the Nullstellensatz