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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| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2016
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/57 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543154322276352 |
|---|---|
| author | Pihura, Oksana Zabavsky, Bohdan |
| author_facet | Pihura, Oksana Zabavsky, Bohdan |
| author_sort | Pihura, Oksana |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2016-01-12T07:40:37Z |
| 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. |
| first_indexed | 2025-12-02T15:36:14Z |
| format | Article |
| id | admjournalluguniveduua-article-57 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:36:14Z |
| publishDate | 2016 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | 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 |
| 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 |
| title | 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_short | A morphic ring of neat range one |
| title_sort | morphic ring of neat range one |
| topic | Bezout ring neat ring clear ring elementary divisor ring stable range one neat range one 13F99 |
| topic_facet | Bezout ring 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/57 |
| work_keys_str_mv | AT pihuraoksana amorphicringofneatrangeone AT zabavskybohdan amorphicringofneatrangeone AT pihuraoksana morphicringofneatrangeone AT zabavskybohdan morphicringofneatrangeone |