On $S$-$n$-absorbing ideals
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910904599183360 |
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| author | Baek, Hyungtae Choi, Hyun Seung Lim, Jung Wook |
| author_facet | Baek, Hyungtae Choi, Hyun Seung Lim, Jung Wook |
| contents | Let $R$ be a commutative ring with identity, $S$ a multiplicative subset of $R$ and $I$ an ideal of $R$ disjoint from $S$. In this paper, we introduce the notion of an $S$-$n$-absorbing ideal which is a generalization of both the $S$-prime ideals and $n$-absorbing ideals. Moreover, we investigate the basic properties, quotient extension, existence and amalgamation of $S$-$n$-absorbing ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_18032 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On $S$-$n$-absorbing ideals Baek, Hyungtae Choi, Hyun Seung Lim, Jung Wook Commutative Algebra 13A15 Let $R$ be a commutative ring with identity, $S$ a multiplicative subset of $R$ and $I$ an ideal of $R$ disjoint from $S$. In this paper, we introduce the notion of an $S$-$n$-absorbing ideal which is a generalization of both the $S$-prime ideals and $n$-absorbing ideals. Moreover, we investigate the basic properties, quotient extension, existence and amalgamation of $S$-$n$-absorbing ideals. |
| title | On $S$-$n$-absorbing ideals |
| topic | Commutative Algebra 13A15 |
| url | https://arxiv.org/abs/2310.18032 |