可换偏序半群的有限全序扩张

On Extensions of Finitely Totally Order of Commutative Partially Ordered Semigroups

设(S,·,≤)是偏序半群,首先定义了S的半拟序σ及模σ的半拟链,其次,通过模σ的半拟链,将S的偏序≤扩张为≤*,并讨论了(S,·,≤*)是偏序半群的充分条件。最后,还给出了S的满足一定条件的有限子集在≤*下成链的充要条件。

Let be mi-pseudochain tending a partial partially ordered semigroups. In this parper, Firstly, the condition for extending a tions of S form a chain. concepts ot semi-pseuaooroer and seSecondly, a sufficient conditions for exgiven. Finally, a sufficient and necessary partial order of S to another partial order suth that some finite subsets satisfying some conditions of S form a chain.