Localization in Noetherian rings / A.V. Jategaonkar.
1986
QA251.4 .J37 1986eb
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Details
Title
Localization in Noetherian rings / A.V. Jategaonkar.
Author
ISBN
9781107361300 (electronic bk.)
1107361303 (electronic bk.)
9780511661938 (e-book)
0511661932 (e-book)
0521317134
9780521317139
1107361303 (electronic bk.)
9780511661938 (e-book)
0511661932 (e-book)
0521317134
9780521317139
Imprint
Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1986.
Language
English
Description
1 online resource (xii, 324 pages) : illustrations
Call Number
QA251.4 .J37 1986eb
System Control No.
(OCoLC)839304875
Summary
This monograph first published in 1986 is a reasonably self-contained account of a large part of the theory of non-commutative Noetherian rings. The author focuses on two important aspects: localization and the structure of infective modules. The former is presented in the opening chapters after which some new module-theoretic concepts and methods are used to formulate a new view of localization. This view, which is one of the book's highlights, shows that the study of localization is inextricably linked to the study of certain injectives and leads, for the first time, to some genuine applications of localization in the study of Noetherian rings. In the last part Professor Jategaonkar introduces a unified setting for four intensively studied classes of Noetherian rings: HNP rings, PI rings, enveloping algebras of solvable Lie algebras, and group rings of polycyclic groups. Some appendices summarize relevant background information about these four classes.
Bibliography, etc. Note
Includes bibliographical references (pages 310-318) and index.
Formatted Contents Note
Cover; Title; Copyright; Contents; PREFACE; TERMINOLOGY AND NOTATION; 1. ORE'S METHOD OF LOCALIZATION, ; 1 .1 Quotient rings, ; 1.2 Transfer of properties to quotient rings, ; 1.3 Noetherian rings: examples, ; 2. ORDERS IN SEMI-SIMPLE RINGS, ; 2 .1 Orders: definition and elementary properties; 2.2 Torsionfree modules over orders in semi-simple rings, ; 2.3 Goldie's Theorem, ; 3. LOCALIZATION AT SEMI-PRIME IDEALS, ; 3 .1 The set (S), ; 3.2 Localizable semi-prime ideals, ; 3.3 Classical localization, ; 3.4 Why Ore's method?; 4. LOCALIZATION, PRIMARY DECOMPOSITION, AND THE SECOND LAYER,
4 .1 Injective modules over Noetherian rings,4.2 Primary decomposition of modules, ; 4.3 Localizability and injectives, ; 4.4 The second layer, ; 5. LINKS, BONDS, AND NOETHERIAN BIMODULES, ; 5.1 Noetherian bimodules, ; 5.2 Bonds, ; 5.3 Links and cliques, ; 5.4 Localizability and stability, ; 6. THE SECOND LAYER, ; 6.1 The dichotomy in the second layer, ; 6.2 Sparsity and local finiteness of the link graph, ; 6.3 Evaluation of multiplicity, ; 7 CLASSICAL LOCALIZATION, ; 7 .1 Classical sets, ; 7.2 Classical cliques, ; 7.3 Classical localization at semi-prime ideals, ; 7.4 Noetherian orders in Artinian rings,
8 THE SECOND LAYER CONDITION,8.1 A hierarchy of Noetherian rings, ; 8.2 In comparability condition and invariants of, ; 8.3 Fully semi-primary rings and Jacobson's conjecture, ; 9 INDECOMPOSABLE INJECTIVES AND THE SECOND LAYER CONDITION, ; 9.1 Fundamental series, ; 9.2 Fundamental prime ideals, ; 9.3 Modules over polynormal rings and centrally separated rings, ; 9.4 Modules over FBN rings, ; APPENDIX: IMPORTANT CLASSES OF NOETHERIAN RINGS, ; A.I Hereditary Noetherian prime rings, ; A.2 Finite algebras and Noetherian P . I . rings, ; A.3. Enveloping algebras of solvable Lie algebras,
A.4. Group rings of polycyclic
by
finite groups, REFERENCES; INDEX
4 .1 Injective modules over Noetherian rings,4.2 Primary decomposition of modules, ; 4.3 Localizability and injectives, ; 4.4 The second layer, ; 5. LINKS, BONDS, AND NOETHERIAN BIMODULES, ; 5.1 Noetherian bimodules, ; 5.2 Bonds, ; 5.3 Links and cliques, ; 5.4 Localizability and stability, ; 6. THE SECOND LAYER, ; 6.1 The dichotomy in the second layer, ; 6.2 Sparsity and local finiteness of the link graph, ; 6.3 Evaluation of multiplicity, ; 7 CLASSICAL LOCALIZATION, ; 7 .1 Classical sets, ; 7.2 Classical cliques, ; 7.3 Classical localization at semi-prime ideals, ; 7.4 Noetherian orders in Artinian rings,
8 THE SECOND LAYER CONDITION,8.1 A hierarchy of Noetherian rings, ; 8.2 In comparability condition and invariants of, ; 8.3 Fully semi-primary rings and Jacobson's conjecture, ; 9 INDECOMPOSABLE INJECTIVES AND THE SECOND LAYER CONDITION, ; 9.1 Fundamental series, ; 9.2 Fundamental prime ideals, ; 9.3 Modules over polynormal rings and centrally separated rings, ; 9.4 Modules over FBN rings, ; APPENDIX: IMPORTANT CLASSES OF NOETHERIAN RINGS, ; A.I Hereditary Noetherian prime rings, ; A.2 Finite algebras and Noetherian P . I . rings, ; A.3. Enveloping algebras of solvable Lie algebras,
A.4. Group rings of polycyclic
by
finite groups, REFERENCES; INDEX
Source of Description
Print version record.
Series
London Mathematical Society lecture note series ; 98.
Available in Other Form
Print version: Jategaonkar, A.V. Localization in Noetherian rings. Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1986
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