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On $n$ $n$ -irreducible ideals of commutative rings

Nabil Zeidi

Nabil Zeidi

Department of Mathematics, Faculty of Sciences, Sfax University B. P. 1171, 3000 Sfax, Tunisia

E-mail Address: zeidi.nabil@gmail.com

E-mail Address: zeidi_nabil@yahoo.com

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https://doi.org/10.1142/S0219498820501200Cited by:1 (Source: Crossref)

Abstract

Let $R$ be a commutative ring with $1 \neq 0$ and $n$ a positive integer. The main purpose of this paper is to study the concepts of $n$ -irreducible and strongly $n$ -irreducible ideals which are generalizations of irreducible and strongly irreducible ideals, respectively. A proper ideal $I$ of $R$ is called $n$ -irreducible (respectively, strongly $n$ -irreducible) if for each ideals $I_{1}, \dots, I_{n + 1}$ of $R$ , $I = I_{1} \cap \dots \cap I_{n + 1}$ (respectively, $I_{1} \cap \dots \cap I_{n + 1} \subseteq I$ ) implies that there are $n$ of the $I_{i}$ ’s whose intersection is $I$ (respectively, whose intersection is in $I$ ).

Communicated by A. Facchini

Keywords:

AMSC: 13A15, 13C05, 13F05

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