摘要
设X是一个非空有限集合,且X=n,TX是X上的全变换半群.取a∈TX,在TX上定义运算*a:对任意的x,y∈TX,有x*ay=xay.易见TX对运算*a构成一个半群,称为有限全变换半群的变种,记作T_X^a.考虑T_X^a及其最大正则子半群Reg(T_X^a),给出T_X^a的极大子半群及Reg(T_X^a)的极大正则子半群的结构与完全分类.
Let X be a nonnull finite set with X =n,TXbe the finite full transformation semigroup on X.We took a∈TX and defined operation *a on TX for arbitrary x,y∈TX,and x*ay=xay.TX constituted a semigroup of the operation *a, which was called a variant of the finite full transformation semigroup,and denoted TX^a.We considered TX^a and its maximal regular subsemigroup Reg(TX^a),and gave the structure and complete classification of maximal subsemigroups of TX^a and maximal regular semigroups of Reg(TX^a).
作者
金久林
游泰杰
徐波
JIN Jiulin;YOU Taijie;XU Bo(School of Mathematical Sciences, Guizhou Normal University, Guiyang 550001 , China)
出处
《吉林大学学报(理学版)》
CAS
CSCD
北大核心
2018年第3期549-555,共7页
Journal of Jilin University:Science Edition
基金
国家自然科学基金(批准号:11461014)
关键词
变换半群
变种
极大正则子半群
矩形群
transformation semigroup
variant
maximal regular subsemigroup
rectangular group