半群Р_(n)(r)的正则性  

The regularity of the semigroup Р_(n)(r)

作　　者：赵颐 戴先胜 ZHAO Yi;DAI Xiansheng(School of Mathematical Sciences,Guizhou Normal University,Guiyang,Guizhou 550025,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550025

出　　处：《贵州师范大学学报（自然科学版）》2024年第6期78-80,90,共4页Journal of Guizhou Normal University：Natural Sciences

基　　金：国家自然科学基金项目(12361005)。

摘　　要：设Р_(n)是X_(n)={1,2,…,n}上的部分变换半群,对任意1≤r≤n-1,记X_(r)={1,…,r},令Р_(n)(r)={α∈Р_(n):X_(r)■dom(α),X_(r)α?X_(r)},则Р_(n)(r)是Р_(n)的子半群。考虑了半群Р_(n)(r)的正则元、左正则元、右正则元,以及这些元素之间的关系。此外,给出Р_(n)(r)是正则半群、左正则半群和右正则半群的充要条件。Let Р_(n) be the partial transformation semigroup on X_(n)={1,2,…,n}.For 1≤r≤n-1,let X_r={1,2,…,r}.Put Р_(n)(r)={α∈Р_(n):X_r■dom(α),X_rα■X_r}.It is obvious that the semigroup Р_(n)(r) is a subsemigroup of Р_(n).In this paper,we shall characterize regular,left regular and right regular elements of Р_(n)(r),and consider the relationships among these elements.Moreover,we present the necessary and sufficient conditions for Р_(n)(r) to be regular,left regular and right regular.

关 键 词：部分变换半群 正则元 左正则元 右正则元 

分 类 号：O152.1[理学—数学]