On free products and amalgams of pomonoids

Bana Al Subaiei, James Renshaw

Published 2013-12-19, updated 2015-05-05Version 2

The study of amalgamation in the category of partially ordered monoids was initiated by Fakhuruddin in the 1980s. In 1986 he proved that, in the category of commutative pomonoids, every absolutely flat commutative pomonoid is a weak amalgmation base and every commutative pogroup is a strong amalgamation base. Some twenty years later, Bulman-Fleming and Sohail in 2011 extended this work to what they referred to as pomonoid amalgams. In particular they proved that pogroups are poamalgmation bases in the category of pomonoids. Sohail, also in 2011, proved that absolutely poflat commutative pomonoids are poamalgmation bases in the category of commutative pomonoids. In the present paper we extend the work on pomonoid amalgams by generalising the work of Renshaw on amalgams of monoids and extension properties of acts over monoids.