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A class of Idempotent-connected quasi-adequate Semigroups

The aim of this paper is to study a class of idempotent-connected quasi-adequate semigroups,so-called super quasi-adequate semigroups.Several characterization of super quasi-adequate semigroups are obtained.In particular,a construction similar to the Hall-Yamada construction for orthodox semigroups is established.Finally,it is proved that a semigroup is a strong super quasi-adequate semigroup if and only if it is isomorphic to the spined product of a band and a C-a semigroup.