T_E(X)的变种半群T_E(X;θ)的若干性质

Some properties of the variant semigroup T_E(X;θ) of T_E(X)

设X是一个非空集合,E是X上的等价关系,TE(X)={f∈TX∶ (a,b)∈E,(f(a),f(b))∈E}.对于半群S中的一个取定元素θ∈S,重新定义S上的运算 为f g=fθg,其中等式右边表示原来的运算,S关于这个新的运算所成的半群称为S的变种半群.本文讨论了TE(X;θ)的Green关系和Symons同余之间的联系.

Let X be a nonempty set and E be an equivalence on X.LetT_E(X)={f∈T_X∶(a,b)∈E,(f(a),f(b))∈E}. For a fixed element θ in the semigroup S,we redefine an operation  of S as fg=fθg,where the right hand of the equation denotes the original operation of the semigroup S.We refer to the semigroup S with respect to the new operation as a variant semigroup of S.In this paper we discuss the connection between Green's relations for T_E(X;θ) and Symons's congruences.