有限全变换半群变种具有某种性质的极大子半群

Maximal Subsemigroups of Some Properties in Variants of Finite Full Transformation Semigroups

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）.