Semilocal Categories and Modules with Semilocal Endomorphism Rings

Description

This book collects and coherently presents the research that has been undertaken since the author’s previous book Module Theory (1998). In addition to some of the key results since 1995, it also discusses the development of much of the supporting material. In the twenty years following the publication of the Camps-Dicks theorem, the work of Facchini, Herbera, Shamsuddin, Puninski, Prihoda and others has established the study of serial modules and modules with semilocal endomorphism rings as one of the promising directions for module-theoretic research. Providing readers with insights into the directions in which the research in this field is moving, as well as a better understanding of how it interacts with other research areas, the book appeals to undergraduates and graduate students as well as researchers interested in algebra. Front Matter ....Pages i-xvi Monoids, Krull Monoids, Large Monoids (Alberto Facchini)....Pages 1-48 Basic Concepts on Rings and Modules (Alberto Facchini)....Pages 49-89 Semilocal Rings (Alberto Facchini)....Pages 91-110 Additive Categories (Alberto Facchini)....Pages 111-163 Spectral Category and Dual Construction (Alberto Facchini)....Pages 165-194 Auslander–Bridger Transpose, Auslander–Bridger Modules (Alberto Facchini)....Pages 195-213 Semilocal Categories and Their Maximal Ideals (Alberto Facchini)....Pages 215-233 Modules of Type ≤ 2. Uniserial Modules (Alberto Facchini)....Pages 235-289 Modules of Finite Type (Alberto Facchini)....Pages 291-326 The Krull–Schmidt Theorem in the Case Two (Alberto Facchini)....Pages 327-378 Serial Modules of Infinite Goldie Dimension (Alberto Facchini)....Pages 379-433 Some Open Problems (Alberto Facchini)....Pages 435-442 Back Matter ....Pages 443-463