Quasi sdf-absorbing ideals in commutative rings
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915986212388864 |
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| author | Leoreanu-Fotea, Violeta Celikel, Ece Yetkin Arabaci, Tarik Tekir, Unsal |
| author_facet | Leoreanu-Fotea, Violeta Celikel, Ece Yetkin Arabaci, Tarik Tekir, Unsal |
| contents | This paper introduces and studies quasi sdf-absorbing ideals as a generalization of sdf-absorbing ideals. We investigate the stability of this property under various constructions, including localization, surjective images, Nagata idealizations, and amalgamations. We establish conditions under which the radical of such ideals is prime and discuss a specific class of rings where quasi sdf-absorption implies the sdf-absorbing primary property. The study concludes with a classification of these ideals in Z and examples distinguishing them from related ideal classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05279 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quasi sdf-absorbing ideals in commutative rings Leoreanu-Fotea, Violeta Celikel, Ece Yetkin Arabaci, Tarik Tekir, Unsal Commutative Algebra 13A15, 13C05, 13C13 This paper introduces and studies quasi sdf-absorbing ideals as a generalization of sdf-absorbing ideals. We investigate the stability of this property under various constructions, including localization, surjective images, Nagata idealizations, and amalgamations. We establish conditions under which the radical of such ideals is prime and discuss a specific class of rings where quasi sdf-absorption implies the sdf-absorbing primary property. The study concludes with a classification of these ideals in Z and examples distinguishing them from related ideal classes. |
| title | Quasi sdf-absorbing ideals in commutative rings |
| topic | Commutative Algebra 13A15, 13C05, 13C13 |
| url | https://arxiv.org/abs/2605.05279 |