Semilocal categories and modules with semilocal endomorphism rings / Alberto Facchini.

Format:

Book

Author/Creator:

Facchini, Alberto, author.

Series:

Progress in mathematics (Boston, Mass.) ; 0743-1643 v. 331.

Progress in mathematics, 0743-1643 ; volume 331

Language:

English

Subjects (All):

Modules (Algebra).

Endomorphism rings.

Physical Description:

xvi, 463 pages : illustrations ; 24 cm.

Place of Publication:

Cham, Switzerland : Birkhäuser/Springer Nature Switzerland AG, [2019]

Summary:

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.

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Contents:

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 finite type

The Krull-Schmidt theorem in the case two

Serial modules of infinite Goldie dimension

Some open problems.

Notes:

Includes bibliographical references and index.

Current copyright fee: GBP34.00 22\1.

Other Format:

Online version: Facchini, Alberto. Semilocal categories and modules with semilocal endomorphism rings.

ISBN:

9783030232832

3030232832

OCLC:

1101985059

Publisher Number:

10.1007/978-3-030-23284-9