Carl Faith

Injective Modules and Injective Quotient Rings (eBook, PDF)

• Format: PDF

Produktbeschreibung

First published in 1982. These lectures are in two parts. Part I, entitled injective Modules Over Levitzki Rings, studies an injective module E and chain conditions on the set A^(E,R) of right ideals annihilated by subsets of E. Part II is on the subject of (F)PF, or (finitely) pseudo-Frobenius, rings [i.e., all (finitely generated) faithful modules generate the category mod-R of all R-modules]. (The PF rings had been introduced by Azumaya as a generalization of quasi-Frobenius rings, but FPF includes infinite products of Prufer domains, e.g., Z w .)

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Produktdetails

• Verlag: Taylor & Francis eBooks
• Seitenzahl: 120
• Erscheinungstermin: 21. August 2019
• Englisch
• ISBN-13: 9781000657319
• Artikelnr.: 57541799

Autorenporträt

Carl Faith

Inhaltsangabe

PREFACE
PART I INJECTIVE MODULES OVER LEVITZKI RINGS
Abstract
1. Introduction
2. Annihilators and the Galois Connection
3. Levitzki Modules
4. Finite Annihilators
5. Sigma Quasi
injective Modules
Appendix
6. Lemmas from Fitting
Krull
Schmidt
7. The Teply
Miller Theorem
8. A
Injective Modules
9. Kasch Rings
10. A
Rings
Appendix
11. Injective Modules Over Nonnoetherian Commutative Rings
11.1 Introduction
11.2 Preliminaries
11.3 Proof of Beck's Theorem
11.4 Commutative Sigma and Delta Rings
11.5 Artinian (Noetherian) Injectives Are Sigma (Delta) Injective
11.6 A
Polynomial Rings Are Polynomials Over A
Rings
Problems
Notes
Acknowledgments
References
PART II INJECTIVE QUOTIENT RINGS OF COMMUTATIVE RINGS
Abstract
1. Introduction
2. Survey of Relevant Background
3. Lemmas
4. Proof of Theorem B
5. Quotient
injective Pre
FPF Rings Are FPF
6. CFPF = FSI
7. FPF Rings with Semilocal Quotient Rings
8. FPF Rings with PF Quotient Rings
9. Note on the Genus of a Module and Generic Families of Rings
10. FP2F and CFP2F Rings and the "Big" Genus
Problems
References
Abbreviations
INDEX.