| Description |
1 online resource |
| Contents |
Preface -- Rings Related to Finite Posets -- Incidence Rings Incidence Rings -- Right Hereditary Rings -- Incidence Rings Modulo the Radical -- Serial and Semidistributive Rings -- Notes and References -- Distributive and Semidistributive rings -- Distributive Modules and Rings -- Semiprime Semidistributive Rings -- Semiperfect Semidistributive Rings -- Right Hereditary SPSD-rings SPSD-rings -- Notes and References -- The Group of Extensions -- Module Constructions Pushout and Pullback -- The Snake Lemma -- Extensions of Modules -- Baer Sum of Extensions -- Properties of Ext – Ext 1 and Extensions -- Additive and Abelian Categories -- Notes and References -- Modules over Semiperfect Rings -- Finitely Generated Modules over Semiperfect Rings -- Stable Equivalence -- Auslander-Bridger Duality -- Almost Split Sequences -- Cogenerators and Some Identities for Finitely Presented Modules -- Pure Submodules and Pure Exact -- Almost Split Sequences over Semiperfect Rings -- Linkage 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 Lemma -- The Kleiner Lemma -- The Main Construction -- Primitive 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 References -- Artinian Rings of Finite Representation Type -- Eisenbud-Griffith's Theorem -- Auslander's Theorem for Right Artinian Rings -- Artinian Semidistributive Rings -- Artinian Hereditary Semidistributive Rings of Finite -- Representation Type -- Notes and References -- (D; O)-species and SPSD-rings of Bounded Representation Type -- Semiperfect Rings of Bounded Representation type -- Ospecies 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 Type -- Right Hereditary SPSD-rings of Bounded Representation Type -- Notes and References -- References -- Index -- Glossary of Ring |
| Summary |
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 |
| Notes |
"A Science Publishers book." |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Noncommutative algebras.
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Rings (Algebra)
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Noncommutative algebras.
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Rings (Algebra)
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| Form |
Electronic book
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| Author |
Gubareni, Nadezhda Mikhaĭlovna, author.
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| ISBN |
1315233045 |
|
1351869876 |
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9781315233048 |
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9781351869874 |
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