Steps in commutative algebra / R.Y. Sharp.

Format:

Book

Author/Creator:

Sharp, R. Y., author.

Series:

London Mathematical Society student texts ; 51.

London Mathematical Society student texts ; 51

Language:

English

Subjects (All):

Commutative algebra.

Physical Description:

1 online resource (xii, 355 pages) : digital, PDF file(s).

Edition:

Second edition.

Place of Publication:

Cambridge : Cambridge University Press, 2000.

Language Note:

English

Summary:

This introductory account of commutative algebra is aimed at advanced undergraduates and first year graduate students. Assuming only basic abstract algebra, it provides a good foundation in commutative ring theory, from which the reader can proceed to more advanced works in commutative algebra and algebraic geometry. The style throughout is rigorous but concrete, with exercises and examples given within chapters, and hints provided for the more challenging problems used in the subsequent development. After reminders about basic material on commutative rings, ideals and modules are extensively discussed, with applications including to canonical forms for square matrices. The core of the book discusses the fundamental theory of commutative Noetherian rings. Affine algebras over fields, dimension theory and regular local rings are also treated, and for this second edition two further chapters, on regular sequences and Cohen-Macaulay rings, have been added. This book is ideal as a route into commutative algebra.

Contents:

Cover; Title; Copyright; Dedication; Contents; Preface to the 1st Edition; Preface to the 2nd Edition; 1 Commutative rings and subrings; 2 Ideals; 3 Prime ideals and maximal ideals; 4 Primary decomposition; 5 Rings of fractions; 6 Modules; 7 Chain conditions on modules; 8 Commutative Noetherian rings; 9 More module theory; 10 Modules over principal ideal domains; 11 Canonical forms for square matrices; 12 Some applications to field theory; 13 Integral dependence on subrings; 14 Afflne algebras over fields; 15 Dimension theory; 16 Regular sequences and grade; 17 Cohen-Macaulay rings

BibliographyIndex

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 345-346) and index.

ISBN:

1-316-08758-1

1-107-36765-4

1-107-36274-1

1-107-36874-X

0-511-62368-2