Semilocal Categories and Modules with Semilocal Endomorphism Rings

ISBN-13: 9783030232832 / Angielski / Twarda / 2019 / 463 str.

Alberto Facchini

Opis

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.

Recenzje

"The monograph under review offers an excellent up-to-date account on the above topics. It is a very well balanced and enjoyable presentation, which may surely capture the attention of both the student looking for an interesting future research topic and the working researcher." (Septimiu Crivei, Mathematical Reviews, December, 2020)

"The book is very useful for specialists working in Ring Theory and Module Theory, as well as for graduate students interested in algebra." (Constantin Nastasescu, zbMATH 1444.18002, 2020)

Spis treści

Monoids, Krull monoids, large monoids.- Basic Concepts on Rings and Modules.- Semilocal rings.- Additive categories.- Spectral Category and dual Construction.- Auslander-Bridger transpose, Auslander-Bridger modules.- Semilocal categories and their maximal ideals.- Modules of type 2. Uniserial modules.- Modules of nite type.- The Krull-Schmidt Theorem in the case two.- Serial modules of innite Goldie dimension.- Some open problems.