Some properties of the variant semigroup T_E(X;θ) of T_E(X)
Sun Lei · 2004
Let X be a nonempty set and E be an equivalence on X.LetT_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 fg=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.