Regularity and Green's relations for a class of semigroups of partial transformations preserving an equivalence
Gao Rong-hai · Journal of Guizhou Normal University · 2008
Let x denote a set X≥3,PX is a the partial transformation semigroup on the set X,for a non-trivial equivalence E on X,let PE(X)={f∈PX:(a,b)∈E,(f(a),f(b))∈E},then PE(X) is a subsemigroup of PX.This paper can start from a special condition: the single equivalence E on X,namely,E=(A×A)∪Δ(X).A is a proper subset of X,with A1,Δ(X)=(x,x):x∈X.This paper discusses the sufficient and essential conditions of the regular element and the regularity of PE(X),and describes the Green's relations for PE(X) and the Green's relations between regular elements for PE(X).