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An equivalent definition of compatibility in pseudo-effect algebras is given, and its relationships with central elements are investigated. Furthermore, pseudo-MV-algebras are characterized among pseudo-effect algebras by means of compatibility.
We prove a Hahn decomposition theorem for modular measures on pseudo-D-lattices. As a consequence, we obtain a Uhl type theorem and a Kadets type theorem concerning compactness and convexity of the closure of the range.
We investigate the existence of a Caratheodory type extension for modular measures defined on lattice-ordered effect algebras.
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