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Fuzzy $h$-ideals of hemirings

Jianming Zhan·Wiesław A. Dudek
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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 $ζ$ 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.

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Jianming Zhan, Wiesław A. Dudek. 2006-05-28. Fuzzy $h$-ideals of hemirings. https://doi.org/10.1016/j.ins.2006.04.005

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