Decomposition of Pseudo-effect Algebras and the Hammer–Sobczyk Theorem

We prove an algebraic and a topological decomposition theorem for complete pseudo-D-lattices (i.e. lattice-ordered pseudo-effect algebras). As a consequence, we obtain a Hammer–Sobczyk type decomposition theorem for group-valued modular measures defined on pseudo-D-lattices and compactness of the range of every (Formula presented.)-valued σ-additive modular measure on a σ-complete pseudo-D-lattice