Abelian extensions of partially ordered partial monoids

In this paper we introduce the notion of a partially ordered partial monoid (po PM), and we study extensions of cancellative po PMs by abelian groups. We concentrate on the so-called central extensions, and prove that every such extension is an F-product of a po PM by an abelian group defined by a cocycle Like in partially ordered groups, the extension can be ordered by means of special sets. We also compare extensions of po PMs with the extensions of their universal groups.