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].
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].
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.
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.
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