Weakly Primal Graded Superideals

Let G be an abelian group and let R be a commutative G-graded super-ring (briefly, graded super-ring) with unity 1 6= 0. We say that a ∈ h(R), where h(R) is the set of homogeneous elements in R, is weakly prime to a graded superideal I of R if 0 6= r a ∈ I , where r ∈ h(R), then r ∈ I . If ν(I ) is the set of homogeneous elements in R that are not weakly prime to I , then we define I to be weakly primal if P = ⊕ g∈G (ν(I )∩R g +ν(I )∩ R g )∪ {0} forms a graded superideal of R. In this paper we study weakly primal graded superideals of R. Moreover, we classify the relationship among the families of weakly prime graded superideals, primal and weakly primal graded superideals of R.