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Tuganbaev, Askar A.,. Arithmetical Rings and Endomorphisms / Askar A. Tuganbaev. — 1 online resource (175 pages). — In English. — <URL:http://elib.fa.ru/ebsco/2157307.pdf>.Record create date: 6/15/2019 Subject: Commutative rings.; Endomorphism rings.; Endomorphisms (Group theory); Modules (Algebra); Rings (Algebra); Algebra.; Endomorphismenring.; Ideal {u2039}Mathematik{u203A}.; Modul.; Ring {u2039}Mathematik{u203A}.; MATHEMATICS / Algebra / Abstract.; Commutative rings; Endomorphism rings; Endomorphisms (Group theory); Modules (Algebra); Rings (Algebra) Collections: EBSCO Allowed Actions: –
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Annotation
This book offers a comprehensive account of not necessarily commutative arithmetical rings, examining structural and homological properties of modules over arithmetical rings and summarising the interplay between arithmetical rings and other rings, whereas modules with extension properties of submodule endomorphisms are also studied in detail. Graduate students and researchers in ring and module theory will find this book particularly valuable.
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Table of Contents
- Preface
- Introduction
- Contents
- Part I: ARITHMETICAL RINGS
- 1. Saturated ideals and localizations
- 2. Finitely generated modules and diagonalizability
- 3. Rings with flat and quasiprojective ideals
- 4. Hermite rings and Pierce stalks
- 5. Bezout rings, Krull dimension
- Part II: EXTENSION OF AUTOMORPHISMS AND ENDOMORPHISMS
- 6. Semi-Artinian and nonsingular modules
- 7. Modules over strongly prime and strongly semiprime rings
- 8. Endomorphism-extendable modules and rings
- 9. Automorphism-invariant modules and rings
- Bibliography
- Index
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