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...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2009
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| Online-Zugang: | FHN01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | xviii, 291 p. ill |
| ISBN: | 9789814287258 |
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| 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 | ||
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| author | Baba, Yoshitomo |
| author_facet | Baba, Yoshitomo |
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| author_sort | Baba, Yoshitomo |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.4 |
| dewey-search | 512/.4 |
| dewey-sort | 3512 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV044637851 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:52Z |
| institution | BVB |
| isbn | 9789814287258 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030035824 |
| oclc_num | 1012698832 |
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| physical | xviii, 291 p. ill |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | World Scientific Pub. Co. |
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| spelling | Baba, Yoshitomo Verfasser aut Classical artinian rings and related topics Yoshitomo Baba, Kiyoichi Oshiro Singapore World Scientific Pub. Co. c2009 xviii, 291 p. ill txt rdacontent c rdamedia cr rdacarrier 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 Artin rings Commutative rings Rings (Algebra) Artinscher Ring (DE-588)4202669-6 gnd rswk-swf Artinscher Ring (DE-588)4202669-6 s 1\p DE-604 Oshiro, Kiyoichi 1943- Sonstige oth Erscheint auch als Druck-Ausgabe 9789814287241 (hbk.) Erscheint auch als Druck-Ausgabe 9814287245 (hbk.) http://www.worldscientific.com/worldscibooks/10.1142/7451#t=toc Verlag URL des Erstveroeffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Baba, Yoshitomo Classical artinian rings and related topics Artin rings Commutative rings Rings (Algebra) Artinscher Ring (DE-588)4202669-6 gnd |
| subject_GND | (DE-588)4202669-6 |
| title | Classical artinian rings and related topics |
| title_auth | Classical artinian rings and related topics |
| title_exact_search | Classical artinian rings and related topics |
| title_full | Classical artinian rings and related topics Yoshitomo Baba, Kiyoichi Oshiro |
| title_fullStr | Classical artinian rings and related topics Yoshitomo Baba, Kiyoichi Oshiro |
| title_full_unstemmed | Classical artinian rings and related topics Yoshitomo Baba, Kiyoichi Oshiro |
| title_short | Classical artinian rings and related topics |
| title_sort | classical artinian rings and related topics |
| topic | Artin rings Commutative rings Rings (Algebra) Artinscher Ring (DE-588)4202669-6 gnd |
| topic_facet | Artin rings Commutative rings Rings (Algebra) Artinscher Ring |
| url | http://www.worldscientific.com/worldscibooks/10.1142/7451#t=toc |
| work_keys_str_mv | AT babayoshitomo classicalartinianringsandrelatedtopics AT oshirokiyoichi classicalartinianringsandrelatedtopics |