Properties of weakly 2-absorbing primal ideals

Let R be a commutative ring with unity (1 = 0). In this paper we introduce the concept of weakly 2-absorbing primal ideal which is a generalization of weakly primal ideal. Let I be a proper ideal of R. An element a E R is defined to be a weakly 2-absorbing prime to I if for any r, s, t E R with 0 = rsta E I, then rs E I or rt E I or st E I. An element a E R is not a weakly 2-absorbing prime to I if there exist r, s, t E R, with 0 = rsta E I, such that rs, rt, st E R \ I. We denote by nu 0(I) the set of all elements in R that are not weakly 2-absorbing prime to I. We define a proper ideal I of R to be a weakly 2-absorbing primal if the set nu 0(I) U {0} forms an ideal of R. Many results concerning weakly 2-absorbing primal ideals and examples of weakly 2-absorbing primal ideals are given.