JP Journal of Algebra, Number Theory and Applications
Volume 38, Issue 2, Pages 109 - 119
(April 2016) http://dx.doi.org/10.17654/NT038020109 |
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ON ALMOST 2-ABSORBING PRIMARY IDEALS IN COMMUTATIVE RINGS
Malik Bataineh and Obaydah Al-Nuserat
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Abstract: Various generalizations of primary ideals of a commutative ring R with have been studied. For example, a proper ideal I of R is a 2-absorbing primary (resp., weakly 2-absorbing primary) if with (resp., implies or or In this paper, we introduce the concept of almost2-absorbing primary ideal as a new generalization of primary ideals. A proper ideal I of R is called an almost 2-absorbing primary ideal of R whenever and then or or A number of results concerning almost 2-absorbing primary ideals such as their properties and their relation among other primary ideals will be given. Also we will classify all rings for which every proper ideal is an almost 2-absorbing primary ideal. |
Keywords and phrases: primary ideal, prime ideal, 2-absorbing ideal, almost prime ideal, almost primary ideal, almost 2-absorbing ideal, almost 2-absorbing primary ideal. |
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