Key points are not available for this paper at this time.
We introduce the notion of weakly commutativity in the class of all additively idempotent semirings. An additively idempotent semiring is weakly commutative if and only if it is a distributive lattice of weakly commutative Formula: see text-Archimedean semirings.
Sarkar et al. (Sat,) studied this question.