ON 2-ABSORBING PRIMARY IDEALS IN COMMUTATIVE RINGS

Title & Authors
ON 2-ABSORBING PRIMARY IDEALS IN COMMUTATIVE RINGS
Badawi, Ayman; Tekir, Unsal; Yetkin, Ece;

Abstract
Let R be a commutative ring with $\small{1{\neq}0}$. 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 $\small{a,b,c{\in}R}$ and $\small{abc{\in}I}$, then $\small{ab{\in}I}$ or $\small{ac{\in}\sqrt{I}}$ or $\small{bc{\in}\sqrt{I}}$. 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;
Language
English
Cited by
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대한수학회지, 2015. vol.52. 1, pp.97-111
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