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.

Updates readers on developments in module theory that have led to current research Features a list of open research problems Broadens our understanding of the directions in which the research in this field is moving Self-contained presentation

Autorentext
Alberto Facchini studied at the University of Padua, getting the Laurea in Matematica magna cum laude in 1977. He has worked at the University of Udine from 1981 to 1999, becoming full professor of Algebra, and then at the University of Padua from 1999 to 2022. At present he is Emeritus Professor at the University of Padua. He also got fellowships to study and do research at the University of Sheffield, Universitat Autònoma de Barcelona, and Centre de Recerca Matemàtica. He has written about 180 scientific publications and has given lectures and talks at conferences in about forty different countries. In 1981 he received the Bonavera Prize in Mathematics. He has been in the editorial boards of about fifteen mathematical journal, among which Bollettino dell'Unione Matematica Italiana, Communications in Algebra, Journal of Algebra and Its Applications, Rendiconti del Circolo Matematico di Palermo, and Rendiconti del Seminario Matematico dell'Università di Padova.

Klappentext

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.

Inhalt
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.