Abstract. McAlister proved that every locally inverse regular semigroup is a locally isomorphic image of a regular Rees matrix semigroup over an inverse semigroup. In this paper, we show how this result can be generalised to a class of locally adequate abundant semigroups.

AMS Subject Classification (1991): 20M10, 20M17

Received September 28, 1995, and in final form June 5, 2000. (Registered under 2749/2009.)