On certain classes of non-embeddable semigroup amalgams

A semigroup amalgam may be viewed as a triple (U; S_1, S_2) of semigroups, where U is the intersection of S_1 and S_2. We call U the core of the amalgam and S_1, S_2 the containing semigroups. We say that (U; S_1, S_2) is embeddable if there exists a semigroup W containing isomorphic copies of S_1 and S_2 that intersect precisely in the image of U. I shall present my recent work on certain classes of non-embeddable semigroup amalgams. In fact, I shall consider the amalgams where the core is an ample semigroup and the containing semigroups are inverse.