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

Let R be a commutative ring with 1 not equal 0. We recall that a proper ideal I of R is called a weakly 2-absorbing primary ideal of R if whenever a, b, c is an element of R and 0 not equal abc is an element of I, then ab is an element of I or ac is an element of root I or bc is an element of root I . 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 delta : I(R) -> I(R) be a function. Then delta is called an expansion function of ideals of R if whenever L, I, J are ideals of R with J subset of I, then L subset of delta(L) and delta(J) subset of delta(1). Let delta be an expansion function of ideals of R. Then a proper ideal I of R (i.e., I is an element of R) is called a weakly 2-absorbing delta-primary ideal if 0 not equal abc is an element of I implies ab is an element of I or ac is an element of delta(1) or bc is an element of delta(1). For example, let delta :I(R)-> I(R) such that delta(1) = root I. Then delta 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 delta-primary ideal of R. A number of results concerning weakly 2-absorbing delta-primary ideals and examples of weakly 2-absorbing delta-primary ideals are given.