Some notes on strongly E*-unitary inverse semigroups

In this paper, we give a direct proof that every strongly inverse semigroup can be embedded into a 0-semidirect product of a semilattice with zero by a group. As a corollary, we obtain a new proof of the structure theory of strongly inverse semigroups described in 1]. We also prove that the strongly inverse semigroups are precisely inverse semigroups equipped with a , idempotent pure prehomomorphism to a primitive inverse semigroup.