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Basic Commutative Algebra cover
IMPORTANT!
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This textbook, set for a one or two semester course in commutative algebra, provides an introduction to commutative algebra at the postgraduate and research levels. The main prerequisites are familiarity with groups, rings and fields. Proofs are self-contained.

The book will be useful to beginners and experienced researchers alike. The material is so arranged that the beginner can learn through self-study or by attending a course. For the experienced researcher, the book may serve to present new perspectives on some well-known results, or as a reference.

Sample Chapter(s)
Chapter 1: Rings and Ideals (199 KB)

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Contents:
  • Rings and Ideals
  • Modules and Algebras
  • Polynomial and Power Series Rings
  • Homological Tools I
  • Tensor, Symmetric and Exterior Algebras
  • Finiteness Conditions
  • Primary Decomposition
  • Filtrations and Completions
  • Numerical Functions
  • Principal Ideal Theorem
  • Integral Extensions
  • Normal Domains
  • Transcendental Extensions
  • Affine Algebras
  • Derivations and Differentials
  • Valuation Rings and Valuations
  • Homological Tools II
  • Homological Dimensions
  • Depth
  • Regular Rings
  • Divisor Class Groups

Readership: Students and researchers in mathematics at the graduate level.