Here we describe the least distributive lattice congruence Formula: see text on an idempotent semiring in general and characterize the varieties Formula: see text, Formula: see text and Formula: see text of all idempotent semirings such that Formula: see text, Formula: see text and Formula: see text, respectively. If Formula: see text, then the multiplicative reduct Formula: see text is a left, right normal band. Every semiring Formula: see text is a spined product of a semiring in Formula: see text and a semiring in Formula: see text with respect to a distributive lattice.
Bhuniya et al. (Thu,) studied this question.