Commutative Rings Dimension Mulitiplicity and homological Methods

Commutative Rings Dimension Mulitiplicity and homological Methods - Stanisław Balcerzyk

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.