ENGLISH

Arithmetical Rings and Endomorphisms

By Askar A. Tuganbaev

Book information

Publisher
de Gruyter
Year
2019
ISBN
3110658895, 9783110658897
Language
english
Format
PDF
Filesize
1 MB (1510899 bytes)
Series
De Gruyter Graduate
Pages
177\177
Time added
2021-09-08 08:49:07

Description

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. Preface Introduction Contents Part I: ARITHMETICAL RINGS 1. Saturated ideals and localizations 1.1 Distributive modules 1.2 Saturated submodules and saturations 1.3 Localizable rings 2. Finitely generated modules and diagonalizability 2.1 Annihilators and finitely generated modules 2.2 Diagonalizable rings 3. Rings with flat and quasiprojective ideals 3.1 Flat modules 3.2 Flat ideals and submodules 3.3 Modules close to projective 4. Hermite rings and Pierce stalks 4.1 Hermite rings 4.2 Pierce stalks 5. Bezout rings, Krull dimension 5.1 Bezout rings and modules 5.2 Rings with Krull dimension Part II: EXTENSION OF AUTOMORPHISMS AND ENDOMORPHISMS 6. Semi-Artinian and nonsingular modules 6.1 Semi-Artinian Modules 6.2 Singular and nonsingular modules 7. Modules over strongly prime and strongly semiprime rings 7.1 Modules over strongly semiprime rings 7.2 Modules over Hereditary Noetherian Prime Rings 8. Endomorphism-extendable modules and rings 8.1 Strongly endomorphism-extendable modules 8.2 Endomorphism-extendable rings 8.3 Rings with endomorphism-extendable cyclic modules 9. Automorphism-invariant modules and rings 9.1 Automorphism-invariant modules 9.2 Automorphism-invariant rings Bibliography [28] [55] [81] [111] [138] [167] [193] Index

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