Description

Book Synopsis

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.

Table of Contents

Rings and Ideals; Modules and Algebras; Polynomials and Power Series Rings; Homological Tools I; Finiteness Conditions; Primary Decomposition; Filtrations and Completion; Numerical Functions; Dimension of Local Rings; Integral Extensions; Normal Domains; Integral Closure in a Finite Field Extension; Transcendental Extensions; Affine and Graded Rings; Valuation Rings and Valuations; Derivations and Differentials; Homological Tools II; Depth and Cohen-Macaulay Rings; Regular Rings; Divisor Class Groups.

Basic Commutative Algebra

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    A Hardback by Balwant Singh

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      Book details

      Publisher World Scientific Publishing Co Pte Ltd
      Published 21 January 2011
      ISBN-13 9789814313612
      978-9814313612
      ISBN-10 9814313610
      Also in:
      Algebra

      Description

      Book Synopsis

      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.

      Table of Contents

      Rings and Ideals; Modules and Algebras; Polynomials and Power Series Rings; Homological Tools I; Finiteness Conditions; Primary Decomposition; Filtrations and Completion; Numerical Functions; Dimension of Local Rings; Integral Extensions; Normal Domains; Integral Closure in a Finite Field Extension; Transcendental Extensions; Affine and Graded Rings; Valuation Rings and Valuations; Derivations and Differentials; Homological Tools II; Depth and Cohen-Macaulay Rings; Regular Rings; Divisor Class Groups.

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