(?, 2)-Primary Ideals of a Commutative Ring

Abstract

Let R be a commutative ring with nonzero identity, let I(R) be the set of all ideals of R and delta: I(R) -> I(R) an expansion of ideals of R defined by I -> delta(I). We introduce the concept of (delta, 2)-primary ideals in commutative rings. A proper ideal I of R is called a (delta, 2)-primary ideal if whenever a, b is an element of R and ab is an element of I, then a(2) is an element of I or b(2) is an element of delta(I). Our purpose is to extend the concept of 2-ideals to (delta, 2)-primary ideals of commutative rings. Then we investigate the basic properties of (delta, 2)-primary ideals and also discuss the relations among (delta, delta-primary, delta-primary and 2-prime ideals.