On the Green's relations of certain partial transformation semigroups
Gao Rong-hai · Journal of Guizhou Normal University · 2009
Let X denote any set |X|≥5,E is a bi-equivalence on X,namely,E=(A×A)∪(B×B)∪Δ(X),among which A and B are proper subsets of X,with |A|1,|B|1,Δ(X)=(x,x):x∈X.PX denots the semigroup of partial transformations on set X,let PE(X)={f∈PX:(a,b)∈E且a,b∈domf,(f(a),f(b))∈E},then PE(X) is a subsemigroup of PX.This paper describes the Green's relations of PE(X).