Amalgamating inverse semigroups over ample semigroups

Abstract

A semigroup amalgam (S; T1, T2) is known to be non-embeddable if T1 and T2 are both groups (completely regular semigroups, Clifford semigroups) but S is not such. We prove some non-embeddability conditions for semigroup amalgams (S; T1, T2) in which T1 and T2 are inverse semigroups but S is not such. We also introduce some sufficient conditions that make the inverse hulls of the copies of S in T1 and T2 isomorphic; making, in turn, the amalgam (S; T1, T2) weakly embeddable.