Almost Primal Ideals in Commutative Rings

Let I be a proper ideal of a commutative ring R. An element a is an element of R is called almost prime to I provided that ra is an element of I 12 (with r is an element of R) implies that r e I. We denote by A(I) the set of all elements of R that are not almost prime to I. I is called an almost primal ideal of R if the set A(I) boolean OR I(2) forms an ideal of R. In this paper we first provide some results on almost primal ideals. We also study the relations among the primal ideals, weakly primal ideals and almost primal ideals of R.