Advances in Rings and Modules.

Cover -- Title page -- Contents -- Preface -- Chains of semiprime and prime ideals in Leavitt path algebras -- 1. Introduction -- 2. Preliminaries -- 3. Semiprime Ideals -- 4. The Kaplansky Conjecture and the Kaplansky Property -- 5. Union-Prime Ideals of Leavitt Path Algebras -- Acknowledgement -- References -- The conditions ( ᵢ), =1,2,3,11,12, in rings, modules, categories, and lattices -- Introduction -- 1. Lattice background -- 2. The conditions ( ᵢ), =1,2,3,11,12, in lattices -- 3. Linear modular lattices -- 4. Lattice preradicals -- 5. Applications to Grothendieck categories and torsion theories -- References -- On -semi discrete modules -- 1. Introduction -- 2. -Supplement Submodules -- 3. -Semi Discrete Modules -- References -- Nonlinear Lie triple higher derivation on triangular algebras -- 1. Introduction -- 2. Triangular Algebras -- 3. Main Result -- 4. Applications -- References -- On universal localization of Noetherian rings -- 1. Examples -- 2. Main Theorems -- 3. Some general results -- References -- A survey of intrinsic extensions of rings -- 1. Intrinsic extensions -- 2. Direct summand intrinsic extensions -- 3. Dense intrinsic extensions -- 4. Ideal intrinsic extensions -- Acknowledgement -- References -- The reduced ring order and lower semi-lattices -- References -- On a category of extensions whose endomorphism rings have at most four maximal ideals -- 1. Introduction -- 2. Modules with a semilocal endomorphism ring -- 3. Uniserial modules -- 4. Isomorphism -- 5. Examples -- 6. Main Theorem -- References -- Tilting cotorsion pairs and pure semisimple rings -- 1. Introduction -- 2. Definitions and Preliminaries -- 3. Main Results -- References -- Twist invariants of graded algebras -- 1. Introduction -- 2. 2-cocycles and twists -- 3. Twist invariants for Γ-graded algebras.

4. The twist invariant for algebras with one quantum cluster -- 5. The twist invariant for quantum nilpotent algebras and quantum Schubert cell algebras -- 6. General twist invariants -- 7. Stability of the \AD-invariant -- 8. Stability of the twist invariants -- References -- Modules invariant under monomorphisms of their envelopes -- 1. Introduction -- 2. Equivalence of invariance under automorphisms and monomorphisms -- 3. Properties of -automorphism invariant modules -- 4. Examples -- References -- Some results and questions on left-right symmetry -- 1. Introduction -- 2. Prime Rings -- 3. WV-Rings -- 4. Direct sums of CS-modules -- 5. All modules are CS -- 6. Continuous, quasi-continuous modules -- 7. PCI-Domains -- References -- Rings in which every unit is a sum of a nilpotent and an idempotent -- 1. Introduction -- 2. Units being nil-clean -- 3. Units being sums of a nilpotent and two idempotents -- Acknowledgments -- References -- Commutators and Anti-Commutators of Idempotents in Rings -- 1. Introduction -- 2. Idempotent Identities of Kato and Koliha-Rakočević -- 3. Rings with Property \hyperlink{prok}K -- 4. Interplay Between Property \hyperlink{prok}K and Property \hyperlink{prokb}\overline{ } -- 5. Commutator Characterizations for 2×2 Matrix Rings -- References -- Distributive hierarchies of binary operations -- 1. Introduction, motivation and philosophy -- 2. Distributive magmas -- 3. Building Magmas from Groups: The defining function and its uses -- 4. Building fields from abelian groups -- 5. Appendix: Distributive Actions and Hierarchy graphs -- References -- Idealizers in Differential Polynomial Rings and Generalized HNP Rings -- 1. Introduction -- 2. Idealizers in differential polynomial rings -- 3. Some overrings of = [ ]+ -- 4. Some open questions about G-HNP rings -- References -- Module hulls-similarities and contrasts.

1. Introduction -- 2. Similarities and Contrasts -- References -- Direct sums of completely almost self-injective modules -- Introduction -- Preliminaries -- Completely almost self-injective modules -- References -- Back Cover.

This volume, dedicated to Bruno J. Müller, a renowned algebraist, is a collection of papers that provide a snapshot of the diversity of themes and applications that interest algebraists today.The papers highlight the latest progress in ring and module research and present work done on the frontiers of the topics discussed.In addition, selected expository articles are included to give algebraists and other mathematicians, including graduate students, an accessible introduction to areas that may be outside their own expertise.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.