Plane modules and distributive rings
Let $A$ be a semiprime ring entire over its center. We prove that the following conditions are equivalent: (a) A is a ring distributive from the right (left); (b) w.gl. $\dim (A) ≤ 1$; moreover, if $M$ is an arbitrary prime ideal of the ring $A$, then $A/M$ is a right Ore set.
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| Datum: | 1993 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1993
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5860 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512079639740416 |
|---|---|
| author | Tuganbaev, A. A. Туганбаев, А. А. Туганбаев, А. А. |
| author_facet | Tuganbaev, A. A. Туганбаев, А. А. Туганбаев, А. А. |
| author_sort | Tuganbaev, A. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:19:18Z |
| description | Let $A$ be a semiprime ring entire over its center. We prove that the following conditions are equivalent:
(a) A is a ring distributive from the right (left); (b) w.gl. $\dim (A) ≤ 1$; moreover, if $M$ is an arbitrary prime ideal of the ring $A$, then $A/M$ is a right Ore set. |
| first_indexed | 2026-03-24T03:23:05Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5860 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:23:05Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/13/6cf64087920439f5dc3a9b124821ca13.pdf |
| spelling | umjimathkievua-article-58602020-03-19T09:19:18Z Plane modules and distributive rings Плоские модули и дистрибутивные кольца Tuganbaev, A. A. Туганбаев, А. А. Туганбаев, А. А. Let $A$ be a semiprime ring entire over its center. We prove that the following conditions are equivalent: (a) A is a ring distributive from the right (left); (b) w.gl. $\dim (A) ≤ 1$; moreover, if $M$ is an arbitrary prime ideal of the ring $A$, then $A/M$ is a right Ore set. Нехай $A$ — півпервинне кільце, ціле над своїм центром. Доведено, що рівносильні такі умови: а) $A$ — дистрибутивне справа (зліва) кільце; б) w. gl. $\dim (A) ≤ 1$, причому якщо $M$ — будь-який первинний ідеал кільця $A$ , то $A/M$— права множина Оре. Institute of Mathematics, NAS of Ukraine 1993-05-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5860 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 5 (1993); 721–724 Український математичний журнал; Том 45 № 5 (1993); 721–724 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5860/8403 https://umj.imath.kiev.ua/index.php/umj/article/view/5860/8404 Copyright (c) 1993 Tuganbaev A. A. |
| spellingShingle | Tuganbaev, A. A. Туганбаев, А. А. Туганбаев, А. А. Plane modules and distributive rings |
| title | Plane modules and distributive rings |
| title_alt | Плоские модули и дистрибутивные кольца |
| title_full | Plane modules and distributive rings |
| title_fullStr | Plane modules and distributive rings |
| title_full_unstemmed | Plane modules and distributive rings |
| title_short | Plane modules and distributive rings |
| title_sort | plane modules and distributive rings |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5860 |
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