Semilocal Categories and Modules with Semilocal Endomorphism Rings - Alberto Facchini

Semilocal Categories and Modules with Semilocal Endomorphism Rings

Buch | Hardcover
XVI, 463 Seiten
2019 | 1st ed. 2019
Springer International Publishing (Verlag)
978-3-030-23283-2 (ISBN)
139,09 inkl. MwSt
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.

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.

"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)

Erscheinungsdatum
Reihe/Serie Progress in Mathematics
Zusatzinfo XVI, 463 p. 8 illus.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 877 g
Themenwelt Mathematik / Informatik Mathematik Allgemeines / Lexika
Mathematik / Informatik Mathematik Algebra
Schlagworte chain rings • direct-sum decompositions • Krull monoids • Krull-Schmidt theorem • local morphisms • semilocal rings • serial modules • serial rings • spectral categories • uniserial modules
ISBN-10 3-030-23283-2 / 3030232832
ISBN-13 978-3-030-23283-2 / 9783030232832
Zustand Neuware
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