Extensions of Brandt semigroups

Abstract

THEOREM. Let (V, o) be an extension of a Brandt semigroup S by an arbitrary semigroup T with zero, 0'. Let S be given the Rees representation S = M°(G; I , 7; A). Then there exists a partial homomorphism w: A—*WA of T* = (T\0') into $i the full symmetric inverse semigroup on I . Let SA and tA denote the domain and range of WA respectively. If -4J3=0' {juxtaposition denoting multiplication in T) either SA^B^O or SA^IB is a single element dA,BFor each ACzT* there exists a mapping \f/A of SA into the group G such that for AB = 0'