Commutative algebra: Noetherian and Non-Noetherian perspectives

✍ Scribed by D. D. Anderson (auth.), Marco Fontana, Salah-Eddine Kabbaj, Bruce Olberding, Irena Swanson (eds.)

• Publisher: Springer-Verlag New York
• Year: 2011
• Tongue: English
• Leaves: 501
• Edition: 1
• Category: Library

✦ Synopsis

Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra. This volume contains a collection of invited survey articles by some of the leading experts in the field. The authors of these chapters are internationally renowned for their important contributions to various aspects of current research in commutative algebra. Some topics presented in the volume include: generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions, tensor products of algebras over fields, as well as many others. This book is intended for researchers and graduate students interested in studying commutative algebra.

✦ Table of Contents

Front Matter....Pages i-viii
Principal-like ideals and related polynomial content conditions....Pages 1-21
Zero-divisor graphs in commutative rings....Pages 23-45
Class semigroups and t-class semigroups of integral domains....Pages 47-76
Forcing algebras, syzygy bundles, and tight closure....Pages 77-99
Beyond totally reflexive modules and back....Pages 101-143
On v -domains: a survey....Pages 145-179
Tensor product of algebras over a field....Pages 181-202
Multiplicative ideal theory in the context of commutative monoids....Pages 203-231
Projectively full ideals and compositions of consistent systems of rank one discrete valuation rings: a survey....Pages 233-249
Direct-sum behavior of modules over one-dimensional rings....Pages 251-275
The defect....Pages 277-318
The use of ultrafilters to study the structure of Prüfer and Prüfer-like rings....Pages 319-333
Intersections of valuation overrings of two-dimensional Noetherian domains....Pages 335-361
Almost perfect domains and their modules....Pages 363-386
Characteristic p methods in characteristic zero via ultraproducts....Pages 387-420
Rees valuations....Pages 421-440
Weak normality and seminormality....Pages 441-480
Back Matter....Pages 481-492

✦ Subjects

Commutative Rings and Algebras; Algebraic Geometry