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# Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

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1572-9176
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# On weakly 2-absorbing δ-primary ideals of commutative rings

• Corresponding author
• Department of Mathematics & Statistics, American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates
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/ Brahim Fahid
Published Online: 2018-11-06 | DOI: https://doi.org/10.1515/gmj-2018-0070

## Abstract

Let R be a commutative ring with $1\ne 0$. We recall that a proper ideal I of R is called a weakly 2-absorbing primary ideal of R if whenever $a,b,c\in R$ and $0\ne abc\in I$, then $ab\in I$ or $ac\in \sqrt{I}$ or $bc\in \sqrt{I}$. In this paper, we introduce a new class of ideals that is closely related to the class of weakly 2-absorbing primary ideals. Let $I\left(R\right)$ be the set of all ideals of R and let $\delta :I\left(R\right)\to I\left(R\right)$ be a function. Then δ is called an expansion function of ideals of R if whenever $L,I,J$ are ideals of R with $J\subseteq I$, then $L\subseteq \delta \left(L\right)$ and $\delta \left(J\right)\subseteq \delta \left(I\right)$. Let δ be an expansion function of ideals of R. Then a proper ideal I of R (i.e., $I\ne R$) is called a weakly 2-absorbing δ-primary ideal if $0\ne abc\in I$ implies $ab\in I$ or $ac\in \delta \left(I\right)$ or $bc\in \delta \left(I\right)$. For example, let $\delta :I\left(R\right)\to I\left(R\right)$ such that $\delta \left(I\right)=\sqrt{I}$. Then δ is an expansion function of ideals of R, and hence a proper ideal I of R is a weakly 2-absorbing primary ideal of R if and only if I is a weakly 2-absorbing δ-primary ideal of R. A number of results concerning weakly 2-absorbing δ-primary ideals and examples of weakly 2-absorbing δ-primary ideals are given.

MSC 2010: 13A05; 13F05

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Accepted: 2017-03-28

Published Online: 2018-11-06

Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X,

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