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  • © 2019

Semilocal Categories and Modules with Semilocal Endomorphism Rings

Birkhäuser

Authors:

(view affiliations)
  • 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

Part of the book series: Progress in Mathematics (PM, volume 331)

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USD 109.00
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  • ISBN: 978-3-030-23284-9
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USD 149.99
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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xvi
  2. Monoids, Krull Monoids, Large Monoids

    • Alberto Facchini
    Pages 1-48
  3. Basic Concepts on Rings and Modules

    • Alberto Facchini
    Pages 49-89
  4. Semilocal Rings

    • Alberto Facchini
    Pages 91-110
  5. Additive Categories

    • Alberto Facchini
    Pages 111-163
  6. Spectral Category and Dual Construction

    • Alberto Facchini
    Pages 165-194
  7. Semilocal Categories and Their Maximal Ideals

    • Alberto Facchini
    Pages 215-233
  8. Modules of Type ≤ 2. Uniserial Modules

    • Alberto Facchini
    Pages 235-289
  9. Modules of Finite Type

    • Alberto Facchini
    Pages 291-326
  10. The Krull–Schmidt Theorem in the Case Two

    • Alberto Facchini
    Pages 327-378
  11. Serial Modules of Infinite Goldie Dimension

    • Alberto Facchini
    Pages 379-433
  12. Some Open Problems

    • Alberto Facchini
    Pages 435-442
  13. Back Matter

    Pages 443-463

About this book

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.

Keywords

  • semilocal rings
  • Krull-Schmidt theorem
  • direct-sum decompositions
  • Krull monoids
  • local morphisms
  • uniserial modules
  • chain rings
  • serial rings
  • serial modules
  • spectral categories

Reviews

“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 Năstăsescu, zbMATH 1444.18002, 2020)

Authors and Affiliations

  • Department of Mathematics “Tullio Levi-Civita”, University of Padova, Padova, Italy

    Alberto Facchini

Bibliographic Information

Buying options

eBook
USD 109.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-23284-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 149.99
Price excludes VAT (USA)
Hardcover Book
USD 149.99
Price excludes VAT (USA)