Injective positively ordered monoids I

International audienceWe define in this paper a certain notion of completeness for a wide class of commutative (pre)ordered monoids (from now on POMs). This class seems to be the natural context for studying structures like measurable function spaces, equidecomposability types of spaces, partially ordered abelian groups and cardinal algebras. Roughly speaking, spaces of measures with values in complete POMs are complete POMs. Furthermore, this notion of completeness makes it possible to characterize injective POMs 'internally'