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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.09961 |
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| _version_ | 1866910945044856832 |
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| author | Farshadifar, F. |
| author_facet | Farshadifar, F. |
| contents | Let R be a commutative ring with identity and M be an R-module. A proper ideal I of R is said to be a $z^\circ$-ideal if for each $a \in I$ the intersection of all minimal prime ideals containing a is contained in I. The purpose of this paper is to introduce the notion of $z^\circ$-submodules of M as an extension of $z^\circ$-ideals of R. Moreover, we investigate some properties of this class of submodules when M is a reduced multiplication R-module. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09961 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $z^\circ$-submodules of a reduced multiplication module Farshadifar, F. Commutative Algebra Let R be a commutative ring with identity and M be an R-module. A proper ideal I of R is said to be a $z^\circ$-ideal if for each $a \in I$ the intersection of all minimal prime ideals containing a is contained in I. The purpose of this paper is to introduce the notion of $z^\circ$-submodules of M as an extension of $z^\circ$-ideals of R. Moreover, we investigate some properties of this class of submodules when M is a reduced multiplication R-module. |
| title | $z^\circ$-submodules of a reduced multiplication module |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2505.09961 |