Injective Modules and Injective Quotient Rings

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.