Fuzzy $h$-ideals of hemirings

Abstract

A 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 $\zeta$ of a hemiring $S$ is a prime fuzzy left (right) $h$-ideal of $S$ if and only if $\zeta$ is two-valued, $\zeta(0) = 1$, and the set of all $x$ in $S$ such that $\zeta(x) = 1$ is a prime (left) right $h$-ideal of $S$. Finally, the similar properties for maximal fuzzy left (right) $h$-ideals of hemirings are considered.