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.
Author(s): Alberto Facchini
Series: Progress in Mathematics #331
Publisher: Birkhäuser
Year: 2019
Language: English
Pages: 473
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
