Commutative Rings: Dimension, Multiplicity and Homological Methods (Mathematics and Its Applications: Numerical Analysis, Statistics and Operational Research) - Softcover

Stanislaw Balcerzyk; Tadeusz Jozefiak

Softcover

ISBN 10: 0470213485 ISBN 13: 9780470213483

Publisher: John Wiley & Sons Inc, 1989

Synopsis

This book completes the important and comprehensive coverage of commutative ring theory, following previous volume "Commutative Noetherian and Krull Rings" (Ellis Horwood Limited, 1989) which covers the fundamentals of commutative ring theory. This volume features the application of homological algebra to purely ring-theoretic problems, including a homological characterization of regular local rings as local rings of finite global dimension. It describes the characterization of the depth of an ideal in terms of Ext functors, as well as local Gorenstein rings as rings of finite injective dimension. The text contains the first of that scope systematic presentation of Cohen-Macaulay and Gorenstein rings in a book form. Each chapter incorporates exercises, the more difficult being furnished with hints. They are also benefited by short notes and references which trace the methods and theorems of the chapter to their source. Readership: mathematics, algebra, commutative rings, algebraic geometry, algebraic number theory.

About this title

Synopsis

This publication completes the comprehensive coverage of commutative ring theory begun in Balcerzyk and Jozefiak's "Commutative Noetherian and Krull Rings" (Ellis Horwood Limited, March 1989). This volume features the application of homological algebra to purely ring-theoretic problems, including an example of the homologous characterisation of regular local rings as local rings of finite global dimension. It describes the intersection multiplicity in terms of Tor functions, the characterisation of the depth of an ideal in terms of Ext functors, as well as local Gorenstein rings of finite injective dimension. The chapters incorporate exercises, the more difficult being furnished with hints. They are also enhanced by short notes and references which trace the methods and theorems of each chapter to its source. The text will be of interest to researchers and students of mathematics, algebra, commutative rings, algebraic geometry and algebraic number theory.

Edition details

• Publisher: John Wiley & Sons Inc
• Publication date: 1989
• Language: English
• ISBN 10: 0470213485
• ISBN 13: 9780470213483
• Binding: Paperback
• Number of pages: 196