Right Bézout ring with waist is a right Hermite ring
We study noncommutative rings in which the Jacobson radical contains a completely prime ideal. It is proved that a right Bézout ring in which the Jacobson radical contains a completely prime ideal is a right Hermite ring. We describe a new class of Bézout rings that are not elementary divisor rings....
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| Date: | 2010 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2010
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2849 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860508834854862848 |
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| author | Gatalevych, A. I. Гаталевич, А. І. |
| author_facet | Gatalevych, A. I. Гаталевич, А. І. |
| author_sort | Gatalevych, A. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T19:38:45Z |
| description | We study noncommutative rings in which the Jacobson radical contains a completely prime ideal. It is proved that a right Bézout ring in which the Jacobson radical contains a completely prime ideal is a right Hermite ring. We describe a new class of Bézout rings that are not elementary divisor rings. |
| first_indexed | 2026-03-24T02:31:31Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-2849 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:31:31Z |
| publishDate | 2010 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/b3/095d0d38d552f66731e8b33a802225b3.pdf |
| spelling | umjimathkievua-article-28492020-03-18T19:38:45Z Right Bézout ring with waist is a right Hermite ring Праве кільце Безу з талією є правим кільцем Ерміта Gatalevych, A. I. Гаталевич, А. І. We study noncommutative rings in which the Jacobson radical contains a completely prime ideal. It is proved that a right Bézout ring in which the Jacobson radical contains a completely prime ideal is a right Hermite ring. We describe a new class of Bézout rings that are not elementary divisor rings. Исследуются некоммутативные кольца, в которых радикал Джекобсона содержит вполне простой идеал. Доказано, что правое кольцо Безу, в котором радикал Джекобсона содержит вполне простой идеал, является правым кольцом Эрмита. Описан новый класс колец Безу, не являющихся кольцами элементарных делителей. Institute of Mathematics, NAS of Ukraine 2010-01-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/2849 Ukrains’kyi Matematychnyi Zhurnal; Vol. 62 No. 1 (2010); 136–138 Український математичний журнал; Том 62 № 1 (2010); 136–138 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/2849/2450 https://umj.imath.kiev.ua/index.php/umj/article/view/2849/2451 Copyright (c) 2010 Gatalevych A. I. |
| spellingShingle | Gatalevych, A. I. Гаталевич, А. І. Right Bézout ring with waist is a right Hermite ring |
| title | Right Bézout ring with waist is a right Hermite ring |
| title_alt | Праве кільце Безу з талією є правим кільцем Ерміта |
| title_full | Right Bézout ring with waist is a right Hermite ring |
| title_fullStr | Right Bézout ring with waist is a right Hermite ring |
| title_full_unstemmed | Right Bézout ring with waist is a right Hermite ring |
| title_short | Right Bézout ring with waist is a right Hermite ring |
| title_sort | right bézout ring with waist is a right hermite ring |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/2849 |
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