Congruence on a class of additive completely simple semiring

It is known that an additive completely simple semiring S, which contains a bi-idempotent, can be constructed by an additive left zero semiring I. a skew-ring R and an additive right zero semiring . In this paper, the admissible triple group, whose three members come from the normal ideal of R and the congruences of I and , is used to characterize the congruences and the congruence lattice on such S.