The objective of this paper is to study the ordered $h$-regular semirings by the properties of their ordered $h$-ideals. It is proved that each $h$-regular ordered semiring is an ordered $h$-regular semiring but the converse does not follow. Important theorems relating to basic properties of the operator clousre and $h$-regular semirings are given. It is also proved that each regular ordered semiring is an ordered $h$-regular semiring but the converse does not hold. The classifications of the left and the right ordered $h$-regular semirings and the left and the right ordered $h$-weakly regular semirings are also presented.

中文翻译：

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有序$ h $ -ideals表征有序$ h $-常规半环

本文的目的是通过有序的$ h $-理想值的性质研究有序的$ h $-规则半环。证明每个$ h $-常规有序半环都是有序$ h $-常规半环，但反之则不成立。给出了与算子clousre和$ h $-规则半环的基本属性有关的重要定理。还证明了每个规则的有序半环都是有序的$ h $-常规半环，但相反情况并不成立。还介绍了左和右有序的$ h $-常规半环和左和右有序的$ h $-弱常规半环的分类。