2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121656A characterization of an $h$-hemiregular hemiring in terms of a fuzzy $h$-ideal is provided. Some properties of prime fuzzy $h$-ideals of $h$-hemiregular hemirings are investigated. It is proved that a fuzzy subset $ζ$ of a hemiring $S$ is a prime fuzzy left (right) $h$-ideal of $S$ if and only if $ζ$ is two-valued, $ζ(0) = 1$, and the set of all $x$ in $S$ such that $ζ(x) = 1$ is a prime (left) right $h$-ideal of $S$. Finally, the similar properties for maximal fuzzy left (right) $h$-ideals of hemirings are considered.Rings and AlgebrasGeneral Mathematics16Y60; 13E05; 03G25text