The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This is the second volume of Algebras, Rings and Modules: Non-commutative Algebras and Rings by M. Hazewinkel and N. Gubarenis, a continuation stressing the more important recent results on advanced topics of the structural theory of associative algebras, rings and modules.
, Nadiya M. Gubareni
Country of Publication:
12 December 2016
Preface Rings Related to Finite Posets Incidence Rings Incidence Rings I (S; D) Right Hereditary Rings A (S; O) Incidence Rings Modulo the Radical Serial and Semidistributive Rings I (S; ; M) Notes and References Distributive and Semidistributive rings Distributive Modules and Rings Semiprime Semidistributive Rings Semiperfect Semidistributive Rings Right Hereditary SPSD-rings SPSD-ringsNotes and References The Group of ExtensionsModule Constructions Pushout and Pullback The Snake Lemma Extensions of Modules Baer Sum of Extensions Properties of Ext1 Ext1 and Extensions Additive and Abelian CategoriesNotes and ReferencesModules over Semiperfect Rings Finitely Generated Modules over Semiperfect RingsStable EquivalenceAuslander-Bridger Duality Almost Split SequencesCogenerators and Some Identities for Finitely Presented ModulesPure Submodules and Pure Exact Almost Split Sequences over Semiperfect RingsLinkage and Duality of Modules over Semiperfect Rings Notes and References Representations of Primitive Posets Representations of Finite Posets Main Canonical Forms of Matrix Problems Trichotomy LemmaThe Kleiner LemmaThe Main ConstructionPrimitive Posets of Infinite Representation Type Primitive Posets of Finite Representation Type Notes and References Representations of Quivers, Species and Finite Dimensional Algebras Finite Quivers and Their Representations Species, Valued Quivers and Valued Graphs Finite Dimensional Algebras and Their Representations Notes and ReferencesArtinian Rings of Finite Representation Type Eisenbud-Griffith's TheoremAuslander's Theorem for Right Artinian Rings Artinian Semidistributive RingsArtinian Hereditary Semidistributive Rings of FiniteRepresentation TypeNotes and ReferencesO-species and SPSD-rings of Bounded Representation TypeSemiperfect Rings of Bounded Representation typeO-species and Tensor Algebras(D; O)-species and Right Hereditary SPSD-rings Representations of (D; O)-species and Mixed Matrix Problems Some Mixed Matrix Problems(D; O)-species of Unbounded Representation Type(D; O)-species of Bounded Representation TypeRight Hereditary SPSD-rings of Bounded Representation Type Notes and ReferencesReferencesIndexGlossary of Ring