The lexicographic product of po-groups and -perfect pseudo effect algebras
arXiv:1211.2464 · doi:10.1007/s10773-013-1568-5
Abstract
We will study the existence of different types of the Riesz Decomposition Property for the lexicographic product of two partially ordered groups. A special attention will be paid to the lexicographic product of the group of the integers with an arbitrary po-group. Then we apply these results to the study of -perfect pseudo effect algebras. We show that the category of strong -perfect pseudo-effect algebras is categorically equivalent to the category of torsion-free directed partially ordered groups with RDP