...restricted semidirect product of a band by S/ξ. The main result contains our recent representation theorem for F - regular semigroups [1], whence McAlister’s characterization of F -inverse semigroups =-=[2]-=-. Finally, we establish that an orthodox semigroup S is a homomorphic image of an F -regular semigroup, if and only if it contains an inverse subsemigroup S 0 such that (i) for each s ∈ S there is s 0...

...er an F -regular semigroup as well as a certain subsemigroup of a restricted semidirect product of a band by S/ξ. The main result contains our recent representation theorem for F - regular semigroups =-=[1]-=-, whence McAlister’s characterization of F -inverse semigroups [2]. Finally, we establish that an orthodox semigroup S is a homomorphic image of an F -regular semigroup, if and only if it contains an ...