Generators and factorisations of transformation semigroups
Peter M. Higgins, John M Howie, Nik Ruškuc · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1998
IfEis the set of idempotents andGthe group of units within a full transformation semigroup ℐx, thenEG = GE = ℐxifXis finite. The question of identifying the subsemigroupEG = GE = 〈G∪E〉in the case whereXis infinite leads to an investigation of interrelations among various naturally occurring subsemigroups ofℐX. In the final section it is shown that precisely two additional elementsµ, vare needed in order thatG∪E∪{µ, v}should generateℐx.