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cover

Algebra

A Graduate Course

I. Martin Isaacs

₹ 1845

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Imprint

American Mathematical Society

Year of Publishing

2010

Number of pages

528

ISBN

9780821852149

Format

Paperback

Language

English

Dimensions

158 x 240 mm

Series

Indian Editions of AMS Titles

Territorial Rights

India,Nepal,Bhutan,Bangladesh,Sri Lanka,Maldives,Pakistan

  • the Book
  • the Author(s)
  • Table of Contents

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.

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I. Martin Isaacs, University of Wisconsin, Madison, Wisconsin, USA
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PART ONE: NON COMMUTATIVE ALGEBRA
  1. Definitions and Examples of Groups
  2. Subgroups and Cosets
  3. Homomorphisms
  4. Group Actions
  5. The Sylow Theorems and p-groups
  6. Permutation Groups
  7. New Groups from Old
  8. Solvable and Nilpotent Groups
  9. Transfer
  10. Operator Groups and Unique Decompositions
  11. Module Theory without Rings
  12. Rings, Ideals, and Modules
  13. Simple Modules and Primitive Rings
  14. Artinian Rings and Projective Modules
  15. An Introduction to Character Theory
PART TWO: COMMUTATIVE ALGEBRA
  1. Polynomial Rings, PIDs, and UFDs
  2. Field Extensions
  3. Galosis Theory
  4. Separability and Inseparability
  5. Cyclotomy and Geometric Constructions
  6. Finite Fields
  7. Roots, Radicals, and Real Numbers
  8. Norms, Traces, and Discriminants
  9. Transcendental Extensions
  10. The Artin-Schreier Theorem
  11. Ideal Theory
  12. Noetherian Rings
  13. Integrality
  14. Dedekind Domains
  15. Algebraic Sets and the Nullstellensatz
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