Quasi-Euclidean duo rings with elementary reduction of matrices
We establish necessary and sufficient conditions under which a class of quasi-Euclidean duo rings coincides with a class of rings with elementary reduction of matrices. We prove that a Bezout duo ring with stable range 1 is a ring with elementary reduction of matrices. It is proved that a semiexchan...
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2015 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155173 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Quasi-Euclidean duo rings with elementary reduction of matrices / O. Romaniv, A. Sagan // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 2. — С. 317-324. — Бібліогр.: 15 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862642402043363328 |
|---|---|
| author | Romaniv, O. Sagan, A. |
| author_facet | Romaniv, O. Sagan, A. |
| citation_txt | Quasi-Euclidean duo rings with elementary reduction of matrices / O. Romaniv, A. Sagan // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 2. — С. 317-324. — Бібліогр.: 15 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | We establish necessary and sufficient conditions under which a class of quasi-Euclidean duo rings coincides with a class of rings with elementary reduction of matrices. We prove that a Bezout duo ring with stable range 1 is a ring with elementary reduction of matrices. It is proved that a semiexchange quasi-duo Bezout ring is a ring with elementary reduction of matrices iff it is a duo ring.
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| first_indexed | 2025-12-01T05:18:40Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155173 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-01T05:18:40Z |
| publishDate | 2015 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Romaniv, O. Sagan, A. 2019-06-16T10:10:59Z 2019-06-16T10:10:59Z 2015 Quasi-Euclidean duo rings with elementary reduction of matrices / O. Romaniv, A. Sagan // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 2. — С. 317-324. — Бібліогр.: 15 назв. — англ. 1726-3255 2010 MSC:13F99. https://nasplib.isofts.kiev.ua/handle/123456789/155173 We establish necessary and sufficient conditions under which a class of quasi-Euclidean duo rings coincides with a class of rings with elementary reduction of matrices. We prove that a Bezout duo ring with stable range 1 is a ring with elementary reduction of matrices. It is proved that a semiexchange quasi-duo Bezout ring is a ring with elementary reduction of matrices iff it is a duo ring. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Quasi-Euclidean duo rings with elementary reduction of matrices Article published earlier |
| spellingShingle | Quasi-Euclidean duo rings with elementary reduction of matrices Romaniv, O. Sagan, A. |
| title | Quasi-Euclidean duo rings with elementary reduction of matrices |
| title_full | Quasi-Euclidean duo rings with elementary reduction of matrices |
| title_fullStr | Quasi-Euclidean duo rings with elementary reduction of matrices |
| title_full_unstemmed | Quasi-Euclidean duo rings with elementary reduction of matrices |
| title_short | Quasi-Euclidean duo rings with elementary reduction of matrices |
| title_sort | quasi-euclidean duo rings with elementary reduction of matrices |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155173 |
| work_keys_str_mv | AT romanivo quasieuclideanduoringswithelementaryreductionofmatrices AT sagana quasieuclideanduoringswithelementaryreductionofmatrices |