ON LOCALLY EHRESMANN SEMIGROUPS

It was first proved by McAlister in 1983 that every locally inverse semigroup is a locally isomorphic image of a regular Rees matrix semigroup over an inverse semigroup and Lawson in 2000 further generalized this result to some special locally adequate semigroups. In this paper, we show how these results can be extended to a class of locally Ehresmann semigroups.