On subamalgams of partially ordered monoids

The study of pomonoid amalgams was initiated by Fakhuruddin in the 1980s and subsequently extended by Bulman-Fleming, Sohail and the authors in the 2000s. We further investigate pomonoids amalgams and in particular we consider the concept of subpomonoid amalgams possessing a suitable ordered version of the unitary property. If [U; T-1, T-2] is an amalgam of subpomonoids of the amalgam [U; S-1, S-2] we consider the question of whether the free product of the pomonoid amalgam [U; T-1, T-2] is poembeddable in the free product of the pomonoid amalgam [U; S-1, S-2], giving a sufficient condition in terms of strongly pounitary subpomonoids.