In this paper we characterize hemirings in which all h-ideals or all fuzzy
h-ideals are idempotent. It is proved, among other results, that every
h-ideal of a hemiring R is idempotent if and only if the lattice of fuzzy
h-ideals of R is distributive under the sum and h-intrinsic product of
fuzzy h-ideals or, equivalently, if and only if each fuzzy h-ideal of R
is intersection of those prime fuzzy h-ideals of R which contain it. We
also define two types of prime fuzzy h-ideals of R and prove that, a
non-constant h-ideal of R is prime in the second sense if and only if each
of its proper level set is a prime h-ideal of R