关于序超半群的左超理想的研究

本文在序超半群中引入了极小左超理想和极大左超理想的概念, 并讨论了它们的一些相关性质. 进一步地, 引入了序超半群的弱素左超理想、拟素左超理想、拟半素左超理想及弱拟素左超理想的概念, 并讨论这四种素超理想之间的关系. 而且通过左超理想和弱~$m$-系刻画了序超半群的弱拟素左超理想. 同时, 借助于$m$-系对序超半群的拟素左超理想给出刻画. 尤其证明了序超半群$S$是强半单的当且仅当$S$的每个左超理想是$S$的包含它的所有拟素左超理想的交.

An Investigation on Left Hyperideals of Ordered Semihypergroups

In this paper, the concepts of minimal and maximal left hyperideals in ordered semihypergroups are introduced, and several related properties are investigated. Furthermore, we introduce the concepts of weakly prime, quasi-prime, quasi-semiprime and weakly quasi-prime left hyperideals of an ordered semihypergroup, and establish the relationship among the four classes of left hyperideals. Moreover, we give some characterizations of weakly quasi-prime left hyperideals by the left hyperideals and weakly $m$-systems. We also characterize the quasi-prime left hyperideals in terms of the $m$-systems. In particular, we prove that an ordered semihypergroup $S$ is strongly semisimple if and only if every left hyperideal of $S$ is the intersection of all quasi-prime left hyperideals of $S$ containing it.