半群PT_(n)(A;θ)的正则性及格林关系  

Regularity and Green's Relations on A Semigroup of PT_(n)(A;θ)

作　　者：秦美青 Qin Meiqing(School of Mathematics and Statistics,Heze University,Heze 274015,China)

机构地区：[1]菏泽学院数学与统计学院,山东菏泽274015

出　　处：《宁夏大学学报（自然科学版）》2021年第1期24-28,共5页Journal of Ningxia University(Natural Science Edition)

基　　金：山东省自然科学基金资助项目(ZR2014AM032);菏泽学院科学研究基金资助项目(XY17KJ01)。

摘　　要：设集合X_(n)={1,2,…,n}并赋予自然序,PT_(n)是集合X_(n)上所有部分变换构成的半群.设A■X_(n)非空,令PT_(n)(A)={α∈PT_(n):imα■A}.在半群PT_(n)(A)上规定运算■:f■g=fθg,则在运算■下,PT_(n)(A)构成一个新的半群,称为它的变种半群.利用正则元及格林关系的定义,讨论了半群PT_(n)(A)的变种半群的正则性,给出了它的变种半群是正则半群的充要条件,并刻画了其变种半群中任意元素间的格林关系,所得结果是半群PT_(n)(A)上相应结果的推广.Let set X_(n)={1,2,…,n}with the natural order.PT_(n) is a semigroup consisting of all partial transformations on set X_(n).Let A■X_(n) non-empty and PT_(n)(A)={α∈PT_(n):imα■A}.Obviously PT_(n)(A)is a subsemigroup of PT_(n).Specify the operation■on the semigroup PT_(n)(A)then under the operation■,PT_(n)(A)forms a semigroup,called its variant semigroup.Using the definitions of regular elements and Green's relations,the regularity of the variant semigroup of semigroup PT_(n)(A)is discussed.The sufficient and necessary conditions for its variant semigroup to be a regular semigroup are given.The Green's relationship between any elements on the variant semigroup of semigroup PT_(n)(A)is characterized,and the result is a generalization of the corresponding results on the semigroup PT_(n)(A).

关 键 词：变种半群 正则元 正则半群 细化 格林关系 

分 类 号：O152.7[理学—数学]