Ring Theory and Its Applications.

Intro -- Preface -- Thoughts on Eggert's Conjecture -- 1. Introduction -- 2. A first try at proving Eggert's conjecture -- 3. Relations with semigroups -- 4. Some plausible and some impossible generalizations -- 5. Some attempts at counterexamples to Eggert's Conjecture for semigroups -- 6. Sketch of the literature -- References -- -Extensions -- 1. Introduction -- 2. -extensions -- 3. Fundamental Properties of -extensions -- 4. Passage via -extensions -- 5. Essential Extensions -- Acknowledgements -- References -- Strongly -Clean Rings with Involutions -- 1. Introduction -- 2. Strongly *-Clean Rings -- 3. Uniqueness for Projections -- 4. Extensions -- References -- QF Rings Characterized by Injectivities: A Survey -- 1. Introduction -- 2. Self-injective rings and QF rings -- 3. Mininjective rings and QF rings -- 4. Simple injective rings and QF rings -- 5. GP-injective rings, P-injective rings and QF rings -- 6. 2-injective rings, F-injective rings, ℵ₀-injective rings and QF rings -- 7. FP-injective rings and QF rings -- 8. Small injective rings and QF rings -- 9. Max-injective rings and QF rings -- 10. IP-injective rings, GIN rings and QF rings -- 11. Relative continuous rings and QF rings -- 12. A graph of injectivities of rings -- Acknowledgments -- References -- Repeated-Root Cyclic and Negacyclic Codes of Length 6 ^{ } -- 1. Introduction -- 2. Constacyclic Codes and Their Duals -- 3. Self-Dual and Complementary-Dual Constacyclic Codes -- 4. Cyclic Codes of Length 6 ^{ } -- 5. Negacyclic Codes of Length 6 ^{ } -- 6. A Classification Of Constacyclic Codes of Length 6 ^{ } -- Acknowledgement -- References -- Cyclically Presented Modules, Projective Covers and Factorizations -- 1. Introduction -- 2. Generalities -- 3. -exactness -- 4. Projective covers of cyclically presented modules -- 5. Cokernels of endomorphisms.

Acknowledgements -- References -- Isomorphisms of Some Quantum Spaces -- 1. Introduction -- 2. General results -- 3. Quantum matrix algebras -- 4. Certain ambiskew polynomial rings -- 5. Jordan matrix algebra -- 6. Quantum Weyl algebras -- Acknowledgements -- References -- Additive Unit Representations in Endomorphism Rings and an Extension of a Result of Dickson and Fuller -- 1. Introduction -- Results -- References -- On a Class of ⊕-Supplemented Modules -- Introduction -- 1. Principally ⊕-Supplemented Modules -- Acknowledgements -- References -- Definable Classes and Mittag-Leffler Conditions -- Acknowledgement -- 1. Mittag-Leffler inverse systems and dual Mittag-Leffler direct systems -- 2. Two natural transformations -- 3. Definability and cotorsion pairs -- 4. Deconstructibility and closure under direct limits -- References -- A Note on Clean Group Algebras -- 1. Introduction -- 2. Clean Group Algebras -- References -- On Dual Baer Modules -- 1. Introduction -- 2. Dual Rickart Modules -- 3. Coretractable and Quasi-Coretractable Modules -- 4. Direct Sums of Dual Baer Modules -- Acknowlegments -- References -- Jacobson's Lemma for Drazin Inverses -- 1. Introduction -- 2. Formula for Drazin Inverse -- 3. Commutation Rules, and Jacobson Pairs -- 4. Clean Elements and Suitable Elements -- References -- Transfer of Certain Properties from Modules to their Endomorphism Rings -- 1. Introduction -- 2. (Quasi-)continuous, extending, and (strongly) FI-extending modules -- 3. (Quasi-)Baer modules and Rickart modules -- 4. D-Rickart, -Rickart, (Zelmanowitz) regular, and endoregular modules -- 5. Applications -- Acknowledgements -- References -- From Boolean Rings to Clean Rings -- 1. Introduction -- 2. Preliminaries -- 3. Structure Theorems and consequences -- 4. Constructions and Examples -- References -- On Right Strongly McCoy Rings -- Introduction.

1. Preliminaries -- 2. Properties of right strongly McCoy rings -- References -- Compatible Ring Structures on Injective Hulls of Finitely Embedded Rings -- 1. Preliminaries -- 2. Results on compatible ring structures on injective hulls -- 3. The characterization -- References -- Good Matrix Gradings from Directed Graphs -- 1. Homomorphisms -- 2. Background on Directed Graphs -- 3. -Extendible Sets and -Essential Sets -- 4. -Grading Sets -- References -- Leavitt Path Algebras Which Are Zorn Rings -- 1. Introduction and Preliminaries -- 2. Leavitt path algebras and C*-algebras which are Zorn rings -- References -- Sheaves That Fail to Represent Matrix Rings -- 1. Introduction -- 2. A diagram of rings -- 3. The first obstruction: sheaves on a site -- 4. The second obstruction: sheaves of rings -- Acknowledgments -- References -- Rings of Invariant Module Type and Automorphism-Invariant Modules -- 1. Introduction -- 2. Basic Facts about Automorphism-invariant Modules -- 3. Results -- 4. Questions -- References.

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