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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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On weakly 2-absorbing δ-primary ideals of commutative rings

Ayman Badawi
  • 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 10. We recall that a proper ideal I of R is called a weakly 2-absorbing primary ideal of R if whenever a,b,cR and 0abcI, then abI or acI or bcI. 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(R) be the set of all ideals of R and let δ:I(R)I(R) be a function. Then δ is called an expansion function of ideals of R if whenever L,I,J are ideals of R with JI, then Lδ(L) and δ(J)δ(I). Let δ be an expansion function of ideals of R. Then a proper ideal I of R (i.e., IR) is called a weakly 2-absorbing δ-primary ideal if 0abcI implies abI or acδ(I) or bcδ(I). For example, let δ:I(R)I(R) such that δ(I)=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.

Keywords: Prime ideal; weakly prime ideal; almost prime ideal

MSC 2010: 13A05; 13F05

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About the article

Received: 2016-05-30

Accepted: 2017-03-28

Published Online: 2018-11-06


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2018-0070.

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