Cancellation ideals of a ring extension
We study properties of cancellation ideals of ring extensions. Let \(R \subseteq S\) be a ring extension. A nonzero \(S\)-regular ideal \(I\) of \(R\) is called a (quasi)-cancellation ideal of the ring extension \(R \subseteq S\) if whenever \(IB = IC\) for two \(S\)-regular (finitely generated) \(R...
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| Дата: | 2021 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2021
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1424 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-14242021-11-09T03:53:16Z Cancellation ideals of a ring extension Tchamna, S. ring extension, cancellation ideal, pullback diagram 13A15, 13A18, 13B02 We study properties of cancellation ideals of ring extensions. Let \(R \subseteq S\) be a ring extension. A nonzero \(S\)-regular ideal \(I\) of \(R\) is called a (quasi)-cancellation ideal of the ring extension \(R \subseteq S\) if whenever \(IB = IC\) for two \(S\)-regular (finitely generated) \(R\)-submodules \(B\) and \(C\) of \(S\), then \(B =C\). We show that a finitely generated ideal \(I\) is a cancellation ideal of the ring extension \(R\subseteq S\) if and only if \(I\) is \(S\)-invertible. Lugansk National Taras Shevchenko University 2021-11-09 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1424 10.12958/adm1424 Algebra and Discrete Mathematics; Vol 32, No 1 (2021) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1424/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1424/562 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1424/924 Copyright (c) 2021 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
ring extension cancellation ideal pullback diagram 13A15 13A18 13B02 |
| spellingShingle |
ring extension cancellation ideal pullback diagram 13A15 13A18 13B02 Tchamna, S. Cancellation ideals of a ring extension |
| topic_facet |
ring extension cancellation ideal pullback diagram 13A15 13A18 13B02 |
| format |
Article |
| author |
Tchamna, S. |
| author_facet |
Tchamna, S. |
| author_sort |
Tchamna, S. |
| title |
Cancellation ideals of a ring extension |
| title_short |
Cancellation ideals of a ring extension |
| title_full |
Cancellation ideals of a ring extension |
| title_fullStr |
Cancellation ideals of a ring extension |
| title_full_unstemmed |
Cancellation ideals of a ring extension |
| title_sort |
cancellation ideals of a ring extension |
| description |
We study properties of cancellation ideals of ring extensions. Let \(R \subseteq S\) be a ring extension. A nonzero \(S\)-regular ideal \(I\) of \(R\) is called a (quasi)-cancellation ideal of the ring extension \(R \subseteq S\) if whenever \(IB = IC\) for two \(S\)-regular (finitely generated) \(R\)-submodules \(B\) and \(C\) of \(S\), then \(B =C\). We show that a finitely generated ideal \(I\) is a cancellation ideal of the ring extension \(R\subseteq S\) if and only if \(I\) is \(S\)-invertible. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2021 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1424 |
| work_keys_str_mv |
AT tchamnas cancellationidealsofaringextension |
| first_indexed |
2024-04-12T06:25:11Z |
| last_indexed |
2024-04-12T06:25:11Z |
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