  Domain operations on semirings have been axiomatised in two different ways:
by a map from an additively idempotent semiring into a boolean subalgebra of
the semiring bounded by the additive and multiplicative unit of the semiring,
or by an endofunction on a semiring that induces a distributive lattice bounded
by the two units as its image. This note presents classes of semirings where
these approaches coincide.
