Let R be a commutative semiring with identity. Let : I(R) → I(R) ∪ {∅} be a function where I(R) is the set of ideals of R. A proper ideal I of R is called -primary if whenever a, b ∈ R, ab ∈ I − (I) implies that either a ∈ I or b ∈ √I. So if we take ∅(I) = ∅ (resp., 0(I) = 0), a -primary ideal is primary (resp., weakly primary). In this paper we study the properties of several generalizations of primary ideals of R.
