型A半群的Vagner-Preston表示  

The Vagner-Preston Representation of a Type-A Semigroup

作　　者：郭茜[1] 喻秉钧[2,3] 

机构地区：[1]成都师范学院数学学院,四川成都610041 [2]四川师范大学数学与软件科学学院,四川成都610066 [3]成都文理学院数学教研室,四川成都610101

出　　处：《四川师范大学学报（自然科学版）》2016年第4期518-521,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11371205)

摘　　要：逆半群的著名的Vagner-Preston表示定理是群的经典Cayley表示定理向逆半群的一个推广.将这个结果进一步推广到了型A半群上,给出了型A半群的Vagner-Preston表示定理,证明了任一型A半群都是某对称逆半群的型A子半群,此结论也体现了型A半群在富足半群中的地位正恰如逆半群在正则半群中的地位.通过2个例子说明,既存在不是型A半群的恰当半群S,使是S的一个表示;也存在不是型A半群的恰当半群S,使不是一个表示.于是就富足半群类而言,该表示不能推广.The famous Vagner-Preston representation theorem of inverse semigroups is a generalization of the classical Cayley rep- resentation of groups to inverse semigroups. In this paper we generalize further it to type-A semigroups and give the Vagner-Preston rep- resentation of type-A semigroups. We prove that any type-A semigroup is a type-h sub-semigroup of the symmetric inverse semigroup. This conclusion also reflects the fact that type-A semigroup in abundant semigroups is as inverse semigroups in regular semigroups. And then, we also give examples to show that, there exist adequate semigroups which are not type-A semigroups, make the mapping a rep- resentations ; and there also exist adequate semigroups which are not type-A semigroups, do not make the mapping representation. So in the class of abundant semigroups it can not be generalized any more.

关 键 词：恰当半群 型A半群 同态 Vagner-Preston表示 

分 类 号：O152.7[理学—数学]