半群的强可分性

Strong splittability over semigroups

目的研究阿基米德半群,π-正则半群等半群类的强可分性。方法将拓扑学中的可分性引入到一些经典的非正则半群类中,与通过断面研究半群的方法相反,利用半群类的性质来研究一个半群。结果若一个半群在阿基米德半群类或π-正则半群类上是强满逐点可分的,则该半群也为同类半群。结论将Marron DJ,Mcmaster TB和Hhnna AJ的结果推广到了非正则半群类。

Aim To study the strong splittability of the semigroup class of archimedean semigroup,π-regular semigroup and so on. Methods The concept of splittability in topology is introudced to some classic non-regular semigroups, by a inverse method with semigroup transversal, research a semigroup by the properties of semigroup classes. Results If a semigroup is strongly pointwise onto-splittable over a class of archimdean semigroups or of-regular semigroups,then the semigroup is also a archimedean semigroup or π-regular semigroup. Conclusion The results of Marron D J, Mcmaster T B and Hanna A J are generalized to non-regular semigroups.