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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2507.09357 |
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| _version_ | 1866908447972261888 |
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| author | Almahariq, Maram |
| author_facet | Almahariq, Maram |
| contents | For the approx.ideal W of the approx.commutative ring R with unity in a descriptive relator space, after introducing the approx. prime ideal in [], this work demonstrates some special properties of the approx.ideals-specifically, the approx.primary ideal, the approx.semi-primary ideal and the approx.1-absorbing primary ideal. A set of theorems related to these concepts is presented. Among them is this important result: If W is an approx.1-absorbing primary ideal, then r(W) is an approx.prime ideal of the approx. ring R. Furthermore, the relationship between these classes is studied: If W is an approx.prime ideal of R, then W is also an approx.primary ideal. Moreover, it turns out that this is an approx.1-absorbing primary ideal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09357 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On approximately ideals: primary and 1-absorbing ideals in descriptive relator spaces Almahariq, Maram Commutative Algebra 54E05, 55P57, 08A05 For the approx.ideal W of the approx.commutative ring R with unity in a descriptive relator space, after introducing the approx. prime ideal in [], this work demonstrates some special properties of the approx.ideals-specifically, the approx.primary ideal, the approx.semi-primary ideal and the approx.1-absorbing primary ideal. A set of theorems related to these concepts is presented. Among them is this important result: If W is an approx.1-absorbing primary ideal, then r(W) is an approx.prime ideal of the approx. ring R. Furthermore, the relationship between these classes is studied: If W is an approx.prime ideal of R, then W is also an approx.primary ideal. Moreover, it turns out that this is an approx.1-absorbing primary ideal. |
| title | On approximately ideals: primary and 1-absorbing ideals in descriptive relator spaces |
| topic | Commutative Algebra 54E05, 55P57, 08A05 |
| url | https://arxiv.org/abs/2507.09357 |