Principal element lattices
Let be a uniformly complete almost -algebra and a natural number . Then is a uniformly complete semiprime -algebra under the ordering and multiplication inherited from with as positive cone.
We describe necessary and sufficient conditions for a direct product and a lexicographic product of partially ordered quasigroups to be a positive quasigroup. Analogous questions for Riesz quasigroups are studied.
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 possessing a certain interpolation property. According to a result of Dvurečenskij and Vettterlein, can be represented as an interval of a unital partially ordered group . We prove that is projectable (strongly projectable) if and only if is projectable (strongly projectable). An analogous result concerning weak homogeneity of and of is shown to be valid.