SUBTRACTIVE EXTENSION OF IDEALS IN SEMIRINGS

In this paper, we (1) obtain the k-closure of ideals and a characterization of subtractive extension of ideals in the semiring Z + ; (2) introduce the concept of closure of an ideal A of a semiring R with respect to an ideal I of R and prove the set of all subtractive extensions of an ideal I of a semiring R is a complete lattice; (3) show that a subtractive extension P of a Q-ideal I in a semiring R is a semiprime ideal if and only if P=I(Q\P) is a semiprime ideal in the quotient semiring R=I(Q):