$ϕ$-$δ$-$S$-primary hyperideals
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916365973061632 |
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| author | Anbarloei, Mahdi |
| author_facet | Anbarloei, Mahdi |
| contents | Among many generalizations of primary hyperideals, weakly $n$-ary primary hyperideals and $n$-ary $S$-primary hyperideals have been studied recently. Let $S$ be an $n$-ary multiplicative set of a commutative Krasner $(m,n)$-hyperring $K$ and, $ϕ$ and $δ$ be reduction and expansion functions of hyperideals of $K$, respectively. The purpose of this paper is to introduce $n$-ary $ϕ$-$δ$-$S$-primary hyperideals which serve as an extension of $S$-primary hyperideals with the help of $ϕ$ and $δ$. We present some main results and examples explaining the sructure of this concept. We examine the relations of $n$-ary $S$-primary hyperideals with other classes of hyperideals and give some ways to connect them. Moreover, we give some characterizations of this notion on direct product of commutative Krasner $(m, n)$-hyperrings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12241 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $ϕ$-$δ$-$S$-primary hyperideals Anbarloei, Mahdi Commutative Algebra Among many generalizations of primary hyperideals, weakly $n$-ary primary hyperideals and $n$-ary $S$-primary hyperideals have been studied recently. Let $S$ be an $n$-ary multiplicative set of a commutative Krasner $(m,n)$-hyperring $K$ and, $ϕ$ and $δ$ be reduction and expansion functions of hyperideals of $K$, respectively. The purpose of this paper is to introduce $n$-ary $ϕ$-$δ$-$S$-primary hyperideals which serve as an extension of $S$-primary hyperideals with the help of $ϕ$ and $δ$. We present some main results and examples explaining the sructure of this concept. We examine the relations of $n$-ary $S$-primary hyperideals with other classes of hyperideals and give some ways to connect them. Moreover, we give some characterizations of this notion on direct product of commutative Krasner $(m, n)$-hyperrings. |
| title | $ϕ$-$δ$-$S$-primary hyperideals |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2408.12241 |