Absolute closure and special amalgamation in pomonoids

I have recently formulated an ordered analogue of Isbell's zigzag theorem for partially ordered monoids (briefly pomonoids). In this talk, I shall discuss the absolute closure for pomonoids-a pomonoid U is called absolutely closed if U coincides with its dominion in every pomonoid extension. My main result shows that, contrary to absolute fatness and amalgamation, the absolute closure of monoids is not affected by the introduction of orders. I also show that absolutely flat pomonoids are special amalgamation bases in the category of all pomonoids.