Decomposition of pseudo-effect algebras and the Hammer-Sobczyk theorem (Q2520721)

The authors present algebraic and topological decompositions for complete pseudo-D-lattices (a pseudo-D-lattice is equivalent to a lattice-ordered pseudo-effect algebra). In particular, they show that every modular complete pseudo-D-lattice is isomorphic to the direct product of an atomless and an atomic one, the latter is isomorphic to the direct product of atomic irreducible ones. As a consequence, for a group-valued modular measure on a pseudo-D-lattice, they obtain a Hammer-Sobczyk-type decomposition theorem (for an exhaustive measure) and (in some cases) the compactness of the range.