A morphic ring of neat range one
We show that a commutative ring \(R\) has neat range one if and only if every unit modulo principal ideal of a ring lifts to a neat element. We also show that a commutative morphic ring \(R\) has a neat range one if and only if for any elements \(a, b \in R\) such that \(aR=bR\) there exist neat ele...
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | English |
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Lugansk National Taras Shevchenko University
2016
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/57 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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admjournalluguniveduua-article-572016-01-12T07:40:37Z A morphic ring of neat range one Pihura, Oksana Zabavsky, Bohdan Bezout ring, neat ring, clear ring, elementary divisor ring, stable range one, neat range one 13F99 We show that a commutative ring \(R\) has neat range one if and only if every unit modulo principal ideal of a ring lifts to a neat element. We also show that a commutative morphic ring \(R\) has a neat range one if and only if for any elements \(a, b \in R\) such that \(aR=bR\) there exist neat elements \(s, t \in R\) such that \(bs=c\), \(ct=b\). Examples of morphic rings of neat range one are given. Lugansk National Taras Shevchenko University 2016-01-12 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/57 Algebra and Discrete Mathematics; Vol 20, No 2 (2015) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/57/pdf Copyright (c) 2016 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2016-01-12T07:40:37Z |
| collection |
OJS |
| language |
English |
| topic |
Bezout ring neat ring clear ring elementary divisor ring stable range one neat range one 13F99 |
| spellingShingle |
Bezout ring neat ring clear ring elementary divisor ring stable range one neat range one 13F99 Pihura, Oksana Zabavsky, Bohdan A morphic ring of neat range one |
| topic_facet |
Bezout ring neat ring clear ring elementary divisor ring stable range one neat range one 13F99 |
| format |
Article |
| author |
Pihura, Oksana Zabavsky, Bohdan |
| author_facet |
Pihura, Oksana Zabavsky, Bohdan |
| author_sort |
Pihura, Oksana |
| title |
A morphic ring of neat range one |
| title_short |
A morphic ring of neat range one |
| title_full |
A morphic ring of neat range one |
| title_fullStr |
A morphic ring of neat range one |
| title_full_unstemmed |
A morphic ring of neat range one |
| title_sort |
morphic ring of neat range one |
| description |
We show that a commutative ring \(R\) has neat range one if and only if every unit modulo principal ideal of a ring lifts to a neat element. We also show that a commutative morphic ring \(R\) has a neat range one if and only if for any elements \(a, b \in R\) such that \(aR=bR\) there exist neat elements \(s, t \in R\) such that \(bs=c\), \(ct=b\). Examples of morphic rings of neat range one are given. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2016 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/57 |
| work_keys_str_mv |
AT pihuraoksana amorphicringofneatrangeone AT zabavskybohdan amorphicringofneatrangeone AT pihuraoksana morphicringofneatrangeone AT zabavskybohdan morphicringofneatrangeone |
| first_indexed |
2025-12-02T15:36:14Z |
| last_indexed |
2025-12-02T15:36:14Z |
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1850411345300684800 |