E[sup *]-dense E-semigroups.

We investigate E[sup *]-dense semi\-groups as analogues of E-dense semigroups for semigroups with zero. We give a characterisation theorem for E[sup *]-dense semigroups whose idempotents form a *-rectangular band. The construction methods of generalised Rees matrix semigroups are employed to provide examples and illustrations. Our results are analogous to those of Weipoltshammer for E-dense semigroups. [ABSTRACT FROM AUTHOR]