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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| Date: | 2021 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2021
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1424 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543138131214336 |
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| author | Tchamna, S. |
| author_facet | Tchamna, S. |
| author_sort | Tchamna, S. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2021-11-09T03:53:16Z |
| 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. |
| first_indexed | 2025-12-02T15:34:50Z |
| format | Article |
| id | admjournalluguniveduua-article-1424 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:34:50Z |
| publishDate | 2021 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| spellingShingle | ring extension cancellation ideal pullback diagram 13A15 13A18 13B02 Tchamna, S. Cancellation ideals of a ring extension |
| title | 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_short | Cancellation ideals of a ring extension |
| title_sort | cancellation ideals of a ring extension |
| topic | ring extension cancellation ideal pullback diagram 13A15 13A18 13B02 |
| topic_facet | ring extension cancellation ideal pullback diagram 13A15 13A18 13B02 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1424 |
| work_keys_str_mv | AT tchamnas cancellationidealsofaringextension |