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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| Date: | 2017 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2017
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/58 |
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| Journal Title: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua: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 |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2017-04-10T07:40:45Z |
| collection |
OJS |
| language |
English |
| topic |
Distributive domain Bezout duo-domain neat ring clear ring elementary divisor ring stable range one neat range one 13F99 |
| 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 |
| topic_facet |
Distributive domain Bezout duo-domain neat ring clear ring elementary divisor ring stable range one neat range one 13F99 |
| format |
Article |
| author |
Bokhonko, Vasylyna Zabavsky, Bohdan Volodymyrovych |
| author_facet |
Bokhonko, Vasylyna Zabavsky, Bohdan Volodymyrovych |
| author_sort |
Bokhonko, Vasylyna |
| title |
A criterion of elementary divisor domain for distributive domains |
| title_short |
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_sort |
criterion of elementary divisor domain for distributive domains |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2017 |
| 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 |
| first_indexed |
2025-07-17T10:32:02Z |
| last_indexed |
2025-07-17T10:32:02Z |
| _version_ |
1837889825016905728 |