Factorial Analog of Distributive Bezout Domains
We investigate Bezout domains in which an arbitrary maximally-nonprincipal right ideal is two-sided. In the case of At(R) Bezout domains, we show that an arbitrary maximally-nonprincipal two-sided right ideal is also a maximally-nonprincipal left ideal.
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| Date: | 2001 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2001
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4376 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510506660397056 |
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| author | Zabavskii, B. V. Забавський, Б. В. |
| author_facet | Zabavskii, B. V. Забавський, Б. В. |
| author_sort | Zabavskii, B. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:27:24Z |
| description | We investigate Bezout domains in which an arbitrary maximally-nonprincipal right ideal is two-sided. In the case of At(R) Bezout domains, we show that an arbitrary maximally-nonprincipal two-sided right ideal is also a maximally-nonprincipal left ideal. |
| first_indexed | 2026-03-24T02:58:05Z |
| format | Article |
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| id | umjimathkievua-article-4376 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:58:05Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/9e/cd56a7a9d3ba1a0eb803bfc9a138339e.pdf |
| spelling | umjimathkievua-article-43762020-03-18T20:27:24Z Factorial Analog of Distributive Bezout Domains Факторіальний аналог дистрибутивних областей Безу Zabavskii, B. V. Забавський, Б. В. We investigate Bezout domains in which an arbitrary maximally-nonprincipal right ideal is two-sided. In the case of At(R) Bezout domains, we show that an arbitrary maximally-nonprincipal two-sided right ideal is also a maximally-nonprincipal left ideal. Досліджуються області Безу, в яких довільний максимально неголовний правий ідеал є двобічним. У випадку $At(R)$ областей Безу показано, що довільний максимально неголовний правий ідеал, який є двобічним, є максимально неголовним лівим ідеалом. Institute of Mathematics, NAS of Ukraine 2001-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4376 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 11 (2001); 1564-1567 Український математичний журнал; Том 53 № 11 (2001); 1564-1567 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4376/5456 https://umj.imath.kiev.ua/index.php/umj/article/view/4376/5457 Copyright (c) 2001 Zabavskii B. V. |
| spellingShingle | Zabavskii, B. V. Забавський, Б. В. Factorial Analog of Distributive Bezout Domains |
| title | Factorial Analog of Distributive Bezout Domains |
| title_alt | Факторіальний аналог дистрибутивних областей Безу |
| title_full | Factorial Analog of Distributive Bezout Domains |
| title_fullStr | Factorial Analog of Distributive Bezout Domains |
| title_full_unstemmed | Factorial Analog of Distributive Bezout Domains |
| title_short | Factorial Analog of Distributive Bezout Domains |
| title_sort | factorial analog of distributive bezout domains |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4376 |
| work_keys_str_mv | AT zabavskiibv factorialanalogofdistributivebezoutdomains AT zabavsʹkijbv factorialanalogofdistributivebezoutdomains AT zabavskiibv faktoríalʹnijanalogdistributivnihoblastejbezu AT zabavsʹkijbv faktoríalʹnijanalogdistributivnihoblastejbezu |