Generalizations of 2-absorbing primary ideals of commutative rings

Abstract

Let R be a commutative ring with 1 not equal 0 and S(R) be the set of all ideals of R. In this paper, we extend the concept of 2-absorbing primary ideals to the context of 0-2-absorbing primary ideals. Let phi : S(R) -> S(R) U null set be a function. A proper ideal I of R is said to be a phi-2-absorbing primary ideal of R if whenever a, b, c is an element of R with abc is an element of I - phi (I) implies ab is an element of I or ac is an element of root I or be E. A number of results concerning phi-2-absorbing primary ideals are given.