Localization in Noetherian rings /

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 whi...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Jategaonkar, A. V.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1986.
Colección:London Mathematical Society lecture note series ; 98.
Temas:
Noetherian rings.
Localization theory.
Anneaux noethériens.
Théorie de la localisation.
MATHEMATICS > Algebra > Intermediate.
Localization theory
Noetherian rings
Lokalisation > Mathematik
Lokalisation
Noetherscher Ring
Álgebra.
Anéis especiais.
Localisation, Théorie de la.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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

Ejemplares similares