Injectivity of (naturally) ordered projection algebras

A projection algebra is a set with an action of the monoid of extended natural numbers with the minimum as the binary operation. Computer scientists use this notion as a convenient means for algebraic specification of process algebras. In this article we consider injectivity of ordered projection algebras, that is partially ordered projection algebras whose action is monotone. We characterize cyclic injective ones as complete posets, and show that injectivity of arbitrary ordered projection algebras is in some sense related to injectivity of naturally ordered projection algebras.