A criterion of elementary divisor domain for distributive domains
In this paper we introduce the notion of the neat range one for Bezout duo-domains. We show that a distributive Bezout domain is an elementary divisor domain if and only if it is a duo-domain of neat range one.
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| Дата: | 2017 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2017
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/58 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543064281055232 |
|---|---|
| author | Bokhonko, Vasylyna Zabavsky, Bohdan Volodymyrovych |
| author_facet | Bokhonko, Vasylyna Zabavsky, Bohdan Volodymyrovych |
| author_sort | Bokhonko, Vasylyna |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2017-04-10T07:40:45Z |
| description | In this paper we introduce the notion of the neat range one for Bezout duo-domains. We show that a distributive Bezout domain is an elementary divisor domain if and only if it is a duo-domain of neat range one. |
| first_indexed | 2025-12-02T15:50:14Z |
| format | Article |
| id | admjournalluguniveduua-article-58 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:50:14Z |
| publishDate | 2017 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-582017-04-10T07:40:45Z A criterion of elementary divisor domain for distributive domains Bokhonko, Vasylyna Zabavsky, Bohdan Volodymyrovych Distributive domain, Bezout duo-domain, neat ring, clear ring, elementary divisor ring, stable range one, neat range one 13F99 In this paper we introduce the notion of the neat range one for Bezout duo-domains. We show that a distributive Bezout domain is an elementary divisor domain if and only if it is a duo-domain of neat range one. Lugansk National Taras Shevchenko University 2017-04-10 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/58 Algebra and Discrete Mathematics; Vol 23, No 1 (2017) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/58/pdf Copyright (c) 2017 Algebra and Discrete Mathematics |
| spellingShingle | Distributive domain Bezout duo-domain neat ring clear ring elementary divisor ring stable range one neat range one 13F99 Bokhonko, Vasylyna Zabavsky, Bohdan Volodymyrovych A criterion of elementary divisor domain for distributive domains |
| title | A criterion of elementary divisor domain for distributive domains |
| title_full | A criterion of elementary divisor domain for distributive domains |
| title_fullStr | A criterion of elementary divisor domain for distributive domains |
| title_full_unstemmed | A criterion of elementary divisor domain for distributive domains |
| title_short | A criterion of elementary divisor domain for distributive domains |
| title_sort | criterion of elementary divisor domain for distributive domains |
| topic | Distributive domain Bezout duo-domain neat ring clear ring elementary divisor ring stable range one neat range one 13F99 |
| topic_facet | Distributive domain Bezout duo-domain neat ring clear ring elementary divisor ring stable range one neat range one 13F99 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/58 |
| work_keys_str_mv | AT bokhonkovasylyna acriterionofelementarydivisordomainfordistributivedomains AT zabavskybohdanvolodymyrovych acriterionofelementarydivisordomainfordistributivedomains AT bokhonkovasylyna criterionofelementarydivisordomainfordistributivedomains AT zabavskybohdanvolodymyrovych criterionofelementarydivisordomainfordistributivedomains |