On $S$-$n$-absorbing ideals

Hyungtae Baek; Hyun Seung Choi; Jung Wook Lim

doi:10.1080/00927872.2025.2479132

On $S$-$n$-absorbing ideals

Commutative Algebra 2025-04-08 v3

Authors: Hyungtae Baek , Hyun Seung Choi , Jung Wook Lim

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Abstract

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.

Keywords

ideal theory monomial ideals commutative ring theory

Cite

@article{arxiv.2310.18032,
  title  = {On $S$-$n$-absorbing ideals},
  author = {Hyungtae Baek and Hyun Seung Choi and Jung Wook Lim},
  journal= {arXiv preprint arXiv:2310.18032},
  year   = {2025}
}

Comments

18pages

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