Subtractive extension of ideals in semirings - Chaudhari, J. N.; Davvaz, B.; Ingale, K. J. (Sarajevo Journal of Mathematics, 2024)
In this paper, we (1) obtain the k-closure of ideals and a characterization of subtractive extension of ideals in the semiring Z_0^+; (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_(QP) is a semiprime ideal in the quotient semiring R/I_(Q).