$\phi$-PRIMARY SUBTRACTIVE IDEALS IN SEMIRINGS

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.