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Classical artinian rings and related topics /
Quasi-Frobenius rings and Nakayama rings were introduced by T Nakayama in 1939. Since then, these classical artinian rings have continued to fascinate ring theorists with their abundance of properties and structural depth. In 1978, M Harada introduced a new class of artinian rings which were later c...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Autor Corporativo: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; Hackensack, N.J. :
World Scientific Pub. Co.,
©2009.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 082 | 0 | 4 | |a 512/.4 |2 22 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Baba, Yoshitomo. | |
| 245 | 1 | 0 | |a Classical artinian rings and related topics / |c Yoshitomo Baba, Kiyoichi Oshiro. |
| 260 | |a Singapore ; |a Hackensack, N.J. : |b World Scientific Pub. Co., |c ©2009. | ||
| 300 | |a 1 online resource (xviii, 291 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file | ||
| 380 | |a Bibliography | ||
| 504 | |a Includes bibliographical references (pages 277-285) and index. | ||
| 505 | 0 | |a 1. Preliminaries. 1.1. Background sketch. 1.2. Semiperfect rings and perfect rings. 1.3. Frobenius algebras, and Nakayama permutations and Nakayama automorphisms of QF-rings. 1.4. Notation in matrix representations of rings -- 2. A theorem of Fuller. 2.1. Improved versions of Fuller's theorem. 2.2. M-simple-injective and quasi-simple-injective modules. 2.3. Simple-injectivity and the condition [symbol][e, g, f]. 2.4. ACC on right annihilator ideals and the condition [symbol][e, g, f]. 2.5. Injectivity and composition length -- 3. Harada rings. 3.1. Definition of Harada rings. 3.2. A dual property of Harada rings. 3.3. The relationships between Harada rings and co-Harada rings -- 4. The structure theory of left Harada rings. 4.1. Left Harada rings of types (#) and (*). 4.2. A construction of left Harada rings as upper staircase factor rings of block extensions of QF-rings. 4.3. The representation of left Harada rings as upper staircase factor rings of block extensions of QF-rings -- 5. Self-duality of left Harada rings. 5.1. Nakayama isomorphisms, weakly symmetric left H-rings and almost self-duality. 5.2. Self-duality and almost self-duality of left Harada rings. 5.3. Koike's example of a QF-ring without a Nakayama automorphism. 5.4. Factor rings of QF-rings with a Nakayama automorphism -- 6. Skew matrix rings. 6.1. Definition of a skew matrix ring. 6.2. Nakayama permutations vs given permutations. 6.3. QF-Rings with a cyclic Nakayama permutation. 6.4. Strongly QF-rings. 6.5. Block extensions of skew matrix rings -- 7. The structure of Nakayama rings. 7.1. Kupisch series and Kupisch well-indexed set via left HRings. 7.2. Nakayama QF-rings. 7.3. A classification of Nakayama rings. 7.4. An example of a Nakayama QF-ring of KNP[symbol]-type. 7.5. The self-duality of Nakayama rings -- 8. Modules over Nakayama rings. 8.1. Characterizations of Nakayama rings by lifting and extending properties -- 9. Nakayama algebras. 9.1. Nakayama algebras over algebraically closed fields. 9.2. Nakayama group algebras -- 10. Local QF-rings. 10.1. Local QF-rings. 10.2. Examples of local QF-rings with radical cubed zero. | |
| 520 | |a Quasi-Frobenius rings and Nakayama rings were introduced by T Nakayama in 1939. Since then, these classical artinian rings have continued to fascinate ring theorists with their abundance of properties and structural depth. In 1978, M Harada introduced a new class of artinian rings which were later called Harada rings in his honour. Quasi-Frobenius rings, Nakayama rings and Harada rings are very closely interrelated. As a result, from a new perspective, we may study the classical artinian rings through their interaction and overlap with Harada rings. The objective of this seminal work is to present the structure of Harada rings and provide important applications of this structure to the classical artinian rings. In the process, we cover many topics on artinian rings, using a wide variety of concepts from the theory of rings and modules. In particular, we consider the following topics, all of which are currently of much interest and ongoing research : Nakayama permutations, Nakayama automorphisms, Fuller's theorem on i-pairs, artinian rings with self-duality, skew-matrix rings, the classification of Nakayama rings, Nakayama group algebras, the Faith conjecture, constructions of local quasi-Frobenius rings, lifting modules, and extending modules. In our presentation of these topics, the reader will be able to retrace the history of artinian rings. | ||
| 588 | 0 | |a Print version record. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Artin rings. | |
| 650 | 0 | |a Commutative rings. | |
| 650 | 0 | |a Rings (Algebra) | |
| 650 | 6 | |a Anneaux artiniens. | |
| 650 | 6 | |a Anneaux commutatifs. | |
| 650 | 6 | |a Anneaux (Algèbre) | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a Artin rings |2 fast | |
| 650 | 7 | |a Commutative rings |2 fast | |
| 650 | 7 | |a Rings (Algebra) |2 fast | |
| 700 | 1 | |a Ōshiro, Kiyoichi, |d 1943- |1 https://id.oclc.org/worldcat/entity/E39PCjGqWgpb4m8Mx8Kt4kCKHP | |
| 710 | 2 | |a World Scientific (Firm) | |
| 758 | |i has work: |a Classical artinian rings and related topics (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGJMVT6c9kFxdbPJ4tYCKm |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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