Injective Modules and Injective Quotient Rings

Carl Faith (Autor)

Buch | Softcover

120 Seiten

1982
Crc Press Inc (Verlag)
978-0-8247-1632-5 (ISBN)

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Part I, 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].

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 .)

Carl Faith

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.

Erscheint lt. Verlag	29.1.1982
Reihe/Serie	Lecture Notes in Pure and Applied Mathematics
Verlagsort	Bosa Roca
Sprache	englisch
Maße	178 x 254 mm
Gewicht	226 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
ISBN-10	0-8247-1632-9 / 0824716329
ISBN-13	978-0-8247-1632-5 / 9780824716325
Zustand	Neuware