Abstract This study pursues an investigation on L-semihypergroups equipped with an L-order. First, the concept of L-ordered L-semihypergroups is introduced by L-posets and L-semihypergroups, and some related results are obtained. Then, prime, weakly prime, and semiprime L-hyperideals of L-ordered L-semihypergroups are studied. Moreover, the relationships among the three types of L-hyperideals are established. Finally, the intra-regular L-ordered L-semihypergroups are characterized in terms of these L-hyperideals. The results of the study show that some well-known results on ordered semihypergroups also hold in the case of L-ordered L-semihypergroups.

中文翻译：

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L-有序的L-半超群

摘要 本研究致力于研究配备 L 阶的 L 半超群。首先，通过L-posets和L-semihypergroups引入了L-ordered L-semihypergroups的概念，并得到了一些相关的结果。然后，研究了L阶L-半超群的素数、弱素数和半素数L-超理想。此外，建立了三种类型的 L-超理想之间的关系。最后，内正则 L 序 L-半超群的特征在于这些 L-超理想。研究结果表明，关于有序半超群的一些众所周知的结果也适用于 L 有序 L-半超群。