Adequate transversals of abundant semigroups (Jim Renshaw, NBSAN York, 25th November 2009)

Abstract: Inverse transversals of regular semigroups were introduced by Blyth & McAlister in the late 70's in connection with their study of split orthodox semigroups. El-Qallali subsequently generalised the notion to adequate subsemigroups of abundant semigroups and it is this generalisation that I will discuss in this talk. After summarising some of the known results for adequate transversals, I will detail some recent joint work (with Jehan Al-Bar) on the structure of transversals where the abundant semigroup is in fact quasi-adequate and where the structure is based on a spined product of left and right adequate semigroups.