Demotions of ideals in commutative rings with applications to normally torsion-freeness
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915562807885824 |
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| author | Nasernejad, Mehrdad Toledo, Jonathan |
| author_facet | Nasernejad, Mehrdad Toledo, Jonathan |
| contents | Let J \subseteq I be ideals in a commutative Noetherian ring R, and r,s \geq 0. We say that J is a demotion of I if I^r J^s = I^{r+s} \cap J^s for all r,s \geq 0. In this paper, we mainly aim to explore this notion in polynomial rings. In particular, we investigate the relation between the demotion property and normal torsion-freeness. Furthermore, we compare the reductions of ideals and demotions of ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16538 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Demotions of ideals in commutative rings with applications to normally torsion-freeness Nasernejad, Mehrdad Toledo, Jonathan Commutative Algebra Let J \subseteq I be ideals in a commutative Noetherian ring R, and r,s \geq 0. We say that J is a demotion of I if I^r J^s = I^{r+s} \cap J^s for all r,s \geq 0. In this paper, we mainly aim to explore this notion in polynomial rings. In particular, we investigate the relation between the demotion property and normal torsion-freeness. Furthermore, we compare the reductions of ideals and demotions of ideals. |
| title | Demotions of ideals in commutative rings with applications to normally torsion-freeness |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2510.16538 |