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http://dx.doi.org/10.4134/BKMS.2014.51.4.1163

ON 2-ABSORBING PRIMARY IDEALS IN COMMUTATIVE RINGS  

Badawi, Ayman (Department of Mathematics & Statistics American University of Sharjah)
Tekir, Unsal (Department of Mathematics Marmara University)
Yetkin, Ece (Department of Mathematics Marmara University)
Publication Information
Bulletin of the Korean Mathematical Society / v.51, no.4, 2014 , pp. 1163-1173 More about this Journal
Abstract
Let R be a commutative ring with $1{\neq}0$. In this paper, we introduce the concept of 2-absorbing primary ideal which is a generalization of primary ideal. A proper ideal I of R is called a 2-absorbing primary ideal of R if whenever $a,b,c{\in}R$ and $abc{\in}I$, then $ab{\in}I$ or $ac{\in}\sqrt{I}$ or $bc{\in}\sqrt{I}$. A number of results concerning 2-absorbing primary ideals and examples of 2-absorbing primary ideals are given.
Keywords
primary ideal; prime ideal; 2-absorbing ideal; n-absorbing ideal;
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1 D. D. Anderson and M. Bataineh, Generalizations of prime ideals, Comm. Algebra 36 (2008), no. 2, 686-696.   DOI   ScienceOn
2 A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. 75 (2007), no. 3, 417-429.   DOI
3 A. Y. Darani and E. R. Puczylowski, On 2-absorbing commutative semigroups and their applications to rings, Semigroup Forum 86 (2013), no. 1, 83-91.   DOI
4 M. Ebrahimpour and R. Nekooei, On generalizations of prime ideals, Comm. Algebra 40 (2012), no. 4, 1268-1279.   DOI
5 R. Gilmer, Multiplicative Ideal Theory, Queen Papers Pure Appl. Math. 90, Queen's University, Kingston, 1992.
6 J. Huckaba, Rings with Zero-Divisors, New York/Basil, Marcel Dekker, 1988.
7 S. Payrovi and S. Babaei, On the 2-absorbing ideals, Int. Math. Forum 7 (2012), no. 5-8, 265-271.
8 D. F. Anderson and A. Badawi, On n-absorbing ideals of commutative rings, Comm. Algebra 39 (2011), no. 5, 1646-1672.   DOI   ScienceOn