Rees matrix covers for a class of locally U-commutative semigroups

摘要

Given the importance of Morita theory of semigroups, we continue the study on the local structure of semigroups. Here we consider a class of nonregular semigroups, called locally U-commutative semigroups having U-local units, containing the classes of locally inverse semigroups, locally adequate semigrouos, locally Ehresmann semigroups, and semigroups with local units having commuting idempotents. Our aim is to give a Rees matrix covering theorem for such semigroups with a partial McAlister sandwich bundle and hence to put all the existing results into one context.