Abstract :
We study amalgamated free products in the category of inverse semigroups. Our approach is combinatorial. Graphical techniques are used to relate the structures of the inverse semigroups in a pushout square, and we then examine amalgamated free products. We show that an amalgam of inverse semigroups strongly embeds in the amalgamated free product, thus providing an alternative proof of the strong amalgamation property for inverse semigroups, a result due to T. E. Hall. We provide sufficient conditions for an amalgamated free product to beE-unitary, and we give necessary and sufficient conditions for the amalgamated free product of a special amalgam to beE-unitary.
