J Austral Math Soc Ser A 48 pp66--78, 1990.
(Received 21 December 1987; revised 23 September 1988)
A semigroup S is called E-inversive if for every a Î S there is an x Î S such that (ax)2 = ax. A construction of all E-inversive subdirect products of two E-inversive semigroups is given using the concept of a subhomomorphism introduced by McAlister and Reilly for inverse semigroups. As an application, E-unitary covers for an E-inversive semigroup are found, in particular for those whose maximum group homomorphic image is a given group. For this purpose, the explicit form of the least group congruence on an arbitrary E-inversive semigroup is given. The special case of full subdirect products of a semilattice and a group (that is, containing all idempotents of the direct product) is investigated and, following an idea of Petrich, a construction of all these semigroups is provided. Finally, all periodic semigroups which are subdirect products of a semilattice or a band with a group are characterized.
1980 AMS Subject Classification (1985 Revision): 20M10
Last Modified: Wed Feb 19 10:27:52 2003