In this paper we deal with a homogeneity condition for an $MV$-algebra concerning a generalized cardinal property. As an application, we consider the homogeneity with respect to $\alpha $-completeness, where $\alpha $ runs over the class of all infinite cardinals.
In this paper we deal with the notions of projectability, spliting property and Dedekind completeness of lattice ordered groups, and with the relations between these notions.
In this paper we deal with a pseudo effect algebra $\Cal A$ possessing a certain interpolation property. According to a result of Dvurečenskij and Vettterlein, $\Cal A$ can be represented as an interval of a unital partially ordered group $G$. We prove that $\Cal A$ is projectable (strongly projectable) if and only if $G$ is projectable (strongly projectable). An analogous result concerning weak homogeneity of $\Cal A$ and of $G$ is shown to be valid.
In this paper we prove that the lateral completion of a projectable lattice ordered group is strongly projectable. Further, we deal with some properties of Specker lattice ordered groups which are related to lateral completeness and strong projectability.