Finite Inverse Semigroups and Amalgamation

Abstract

Given that the class of all inverse semigroups has the (strong) amalgamation property, and that the class of finite inverse semigroups does not, we consider the question of which inverse semigroups are amalgamation bases in the latter class, and we find that they are precisely finite inverse, semigroups whose partially ordered sets of I-classes are chains. Some background results are also given.