Rings Close to Regular:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2002
|
| Schriftenreihe: | Mathematics and Its Applications
545 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Preface All rings are assumed to be associative and (except for nilrings and some stipulated cases) to have nonzero identity elements. A ring A is said to be regular if for every element a E A, there exists an element b E A with a = aba. Regular rings are well studied. For example, [163] and [350] are devoted to regular rings. A ring A is said to be tr-regular if for every element a E A, there is an element n b E A such that an = anba for some positive integer n. A ring A is said to be strongly tr-regular if for every a E A, there is a positive integer n with n 1 n an E a + An Aa +1. It is proved in [128] that A is a strongly tr-regular ring if and only if for every element a E A, there is a positive integer m with m 1 am E a + A. Every strongly tr-regular ring is tr-regular [38]. If F is a division ring and M is a right vector F-space with infinite basis {ei}~l' then End(MF) is a regular (and tr-regular) ring that is not strongly tr-regular. The factor ring of the ring of integers with respect to the ideal generated by the integer 4 is a strongly tr-regular ring that is not regular |
| Beschreibung: | 1 Online-Ressource (XII, 350 p) |
| ISBN: | 9789401598781 9789048161164 |
| DOI: | 10.1007/978-94-015-9878-1 |
Internformat
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| 490 | 0 | |a Mathematics and Its Applications |v 545 | |
| 500 | |a Preface All rings are assumed to be associative and (except for nilrings and some stipulated cases) to have nonzero identity elements. A ring A is said to be regular if for every element a E A, there exists an element b E A with a = aba. Regular rings are well studied. For example, [163] and [350] are devoted to regular rings. A ring A is said to be tr-regular if for every element a E A, there is an element n b E A such that an = anba for some positive integer n. A ring A is said to be strongly tr-regular if for every a E A, there is a positive integer n with n 1 n an E a + An Aa +1. It is proved in [128] that A is a strongly tr-regular ring if and only if for every element a E A, there is a positive integer m with m 1 am E a + A. Every strongly tr-regular ring is tr-regular [38]. If F is a division ring and M is a right vector F-space with infinite basis {ei}~l' then End(MF) is a regular (and tr-regular) ring that is not strongly tr-regular. The factor ring of the ring of integers with respect to the ideal generated by the integer 4 is a strongly tr-regular ring that is not regular | ||
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Datensatz im Suchindex
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401598781 9789048161164 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859588 |
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| physical | 1 Online-Ressource (XII, 350 p) |
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| spelling | Tuganbaev, Askar Verfasser aut Rings Close to Regular by Askar Tuganbaev Dordrecht Springer Netherlands 2002 1 Online-Ressource (XII, 350 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 545 Preface All rings are assumed to be associative and (except for nilrings and some stipulated cases) to have nonzero identity elements. A ring A is said to be regular if for every element a E A, there exists an element b E A with a = aba. Regular rings are well studied. For example, [163] and [350] are devoted to regular rings. A ring A is said to be tr-regular if for every element a E A, there is an element n b E A such that an = anba for some positive integer n. A ring A is said to be strongly tr-regular if for every a E A, there is a positive integer n with n 1 n an E a + An Aa +1. It is proved in [128] that A is a strongly tr-regular ring if and only if for every element a E A, there is a positive integer m with m 1 am E a + A. Every strongly tr-regular ring is tr-regular [38]. If F is a division ring and M is a right vector F-space with infinite basis {ei}~l' then End(MF) is a regular (and tr-regular) ring that is not strongly tr-regular. The factor ring of the ring of integers with respect to the ideal generated by the integer 4 is a strongly tr-regular ring that is not regular Mathematics Algebra Associative Rings and Algebras Mathematik https://doi.org/10.1007/978-94-015-9878-1 Verlag Volltext |
| spellingShingle | Tuganbaev, Askar Rings Close to Regular Mathematics Algebra Associative Rings and Algebras Mathematik |
| title | Rings Close to Regular |
| title_auth | Rings Close to Regular |
| title_exact_search | Rings Close to Regular |
| title_full | Rings Close to Regular by Askar Tuganbaev |
| title_fullStr | Rings Close to Regular by Askar Tuganbaev |
| title_full_unstemmed | Rings Close to Regular by Askar Tuganbaev |
| title_short | Rings Close to Regular |
| title_sort | rings close to regular |
| topic | Mathematics Algebra Associative Rings and Algebras Mathematik |
| topic_facet | Mathematics Algebra Associative Rings and Algebras Mathematik |
| url | https://doi.org/10.1007/978-94-015-9878-1 |
| work_keys_str_mv | AT tuganbaevaskar ringsclosetoregular |