Abstract. For an inverse semigroup $S$, we prove that the translational hull of the closure of the idempotents $\Omega(E_S\omega )$ is isomorphic to the closure of the idempotents $E_{\Omega(S)}\omega $ in the translational hull $\Omega(S)$. This characterization gives a new proof for the fact that the translational hull of an $E\omega $-Clifford semigroup is $E\omega $-Clifford, which was first proved by Reilly [3].

AMS Subject Classification (1991): 20M15, 20M18, 20M12

Received October 1, 1993. (Registered under 5573/2009.)