Research ArticleNo Access

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

K. Alhazmy

Department of Mathematics, Faculty of Sciences, King Khalid University, P. O. Box 9004, Abha, Saudi Arabia

E-mail Address: khazmy@kku.edu.sa

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F. A. A. Almahdi

Department of Mathematics, Faculty of Sciences, King Khalid University, P. O. Box 9004, Abha, Saudi Arabia

E-mail Address: fuadalialmahdy@hotmail.com

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E. M. Bouba

Department of Mathematics and Computer, Faculty Multidisciplinary of Nador, University Mohammed First, Morocco

E-mail Address: mehdi8bouba@hotmail.fr

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, and

M. Tamekkante

https://orcid.org/0000-0002-6947-5464

Department of Mathematics, Faculty of Science, University Moulay Ismail Meknes, Box 11201 Zitoune, Morocco

E-mail Address: tamekkante@yahoo.fr

Corresponding author.

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https://doi.org/10.1142/S0219498824501366Cited by:0 (Source: Crossref)

Abstract

A proper ideal $I$ $I$ of a commutative ring $R$ $R$ is said to be a strongly quasi-primary ideal if, whenever $a, b \in R$ $a, b \in R$ with $a b \in I$ $a b \in I$ , then $a^{2} \in I$ $a^{2} \in I$ or $b \in \sqrt{I}$ $b \in \sqrt{I}$ (see [S. Koc, U. Tekir and G. Ulucak, On strongly quasi primary ideals, Bull. Korean Math. Soc. 56(3) (2019) 729–743]). This paper studies the class of strongly quasi-primary ideals with a radical equal to the nil-radical of $R$ $R$ , called the class of quasi- $n$ $n$ -ideals. Among other results, this new class of ideals is used to characterize when the nil-radical of $R$ $R$ is a maximal or a minimal ideal of $R$ $R$ . Many examples are given to illustrate the obtained results.

Communicated by E. Gorla

Keywords:

AMSC: 13A15, 13A99

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