Green's *-Relations and Abundance of the Semigroup PT(X,A)
Let X be a non-empty set and A a non-empty subset of X,and PT(X)the semigroup of all partial transformations on X.Let PT(X,A)={f ∈ PT(X)| imf C A}.Then PT(X,A)is a subsemigroup of PT(X).On the basis of the existing results,we gives some characteristics of the Green*-relations L*and R*on the semigroup PT(X,A),and then studies the abundance of the PT(X,A).
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