Ring Theory

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This book is meant to be used as a first course in ring theory. No pre-requisite, other then an elementary knowledge of mathematics, is necessary. Rigorous proofs are provided for nearly every result.

[edit] Table of contents

Introduction
    • Rings
    • Properties of rings
    • Integral domains and Fields
    • Subrings
    • Idempotent and Nilpotent elements
    • Characteristic of a ring
    • Ideals in a ring
    • Simple ring
  1. Homomorphisms
    • Homomorphisms of rings
    • Theorems on homomorphisms
    • Quotient rings
    • Imbedding of rings
    • Maximal and Prime Ideals
    • Divisibility in rings
  2. Some special domains
    • Principal Ideal Domains
    • Euclidean domains
    • Polynomial rings
    • Unique Factorization domain
    • Primitive and irreducible polynomials
    • R(x) as a UFD
  3. Extension fields
    • Extension fields
    • Field adjunctions
    • Algebraic elements and algebraic extensions
    • Roots of polynomials
    • Constructions by ruler and compass

[edit] Resources

  • GNU Free Documentation License
  • http://www.polya.uklinux.net/rings.pdf
Retrieved from "http://en.wikibooks.org/wiki/Ring_Theory"
Subjects: Ring Theory | Algebra | University level mathematics books
Hidden categories: Alphabetical/R | Dewey/500 | Library of Congress/QA150
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