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 a theorem on weak homogeneity of $MV$-algebras which generalizes a known result on weak homogeneity of Boolean algebras. Further, we consider a homogeneity condition for $MV$-algebras which is defined by means of an increasing cardinal property.
In this paper we deal with weakly homogeneous direct factors of lattice ordered groups. The main result concerns the case when the lattice ordered groups under consideration are archimedean, projectable and conditionally orthogonally complete.