Locally Factorisable Transformation Semigroups

A semigroup S is factorisable if S = GE = EG where G is a subgroup of S and E is the set of idempotents in S; and S is locally factorisable if eSe is factorisable for every e E. In this paper, we unify and extend results which characterise when certain transformation semigroups defined on a set are (locally) factorisable, and we consider the corresponding problem for the semigroup of linear transformations of a vector space.To Yupaporn Kemprasit, mentor of semigroup theorists in Thailand1991 Mathematics Subject Classification: 20M20The third section of this paper formed part of an MSc supervised by the first author. She greatly appreciates the help of her supervisor in this work; and the first two authors are grateful for the assistance of the third author in the preparation of this paper. The third author also acknowledges the generous support of Centro de Mathematica, Universidade do Minho, Portugal, during his visit in July–August 2000 when the paper was completed.