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Note on strongly quasi-primary ideals

University of Hafr AL Batin, Faculty of Sciences, Department of Mathematics, P. O. Box 1803, Hafr Al Batin, Saudi Arabia

E-mail Address: iealshamari@uhb.edu.sa

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Rania Kammoun

University of Hafr AL Batin, Faculty of Sciences, Department of Mathematics, P. O. Box 1803, Hafr Al Batin, Saudi Arabia

E-mail Address: raniakammoun32@gmail.com

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Abdellah Mamouni

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

E-mail Address: a.mamouni.fste@gmail.com

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, and

Mohammed Tamekkante

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

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

E-mail Address: tamekkante@yahoo.fr

Corresponding author.

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https://doi.org/10.1142/S0219498822502012Cited by:0 (Source: Crossref)

Abstract

Let $R$ be a commutative ring with $1 \neq 0$ . A proper ideal $I$ of $R$ is said to be a strongly quasi-primary ideal if, whenever $a, b \in R$ with $a b \in I$ , then either $a^{2} \in I$ or $b \in \sqrt{I}$ . In this paper, we characterize Noetherian and reduced rings over which every (respectively, nonzero) proper ideal is strongly quasi-primary. We also characterize ring over which every strongly quasi primary ideal of $R$ is prime. Many examples are given to illustrate the obtained results.

Communicated by E. Gorla

Keywords:

AMSC: 13A15, 13C05

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