Factorisable Semigroups of Linear Transformations

Let P(X) be the semigroup of all partial transformations of a set X, A subsemigroup S of P(X) is factorisable if S = GE = EH, where G, H are subgroups of S and E is the set of idempotents in S. In 2001, Jampachon, Saichalee and Sullivan proved a simple result that generalized most of the previous work on factorisable subsemigroups of P(X). They also determined when the semigroup T(V) of all linear transformations of a vector space V is factorisable. In this paper, we extend that work to partial linear transformations of V and consider the notion of locally factorisable for such semigroups.