Blocks of pseudo-effect algebras with the Riesz interpolation property

 Pseudo-effect algebras are partial algebras (E;+,0,1) with a partially defined sum + which is not necessary commutative only associative and with two complements, left and right ones. They are a generalization of effect algebras and of orthomodular posets as well as of (pseudo) MV-algebras. We define three kinds of compatibilities of elements and we show that if a pseudo-effect algebra satisfies the Riesz interpolation property, and another natural condition, then every maximal set of strongly compatible elements, called a block, is a pseudo MV-subalgebra, and the pseudo-effect algebra can be covered by blocks. Blocks correspond to Boolean subalgebras of orthomodular posets. Dedicated to Prof. Ján Jakubík on the occasion of his 80th birthday The paper has been supported by the grant VEGA 2/3163/23 SAV, Bratislava, Slovakia, and the fellowship of the Alexander von Humboldt Foundation, Bonn, Germany. The author is thankful the Alexander von Humboldt Foundation for organizing his stay at University of Ulm, Ulm, summer 2001, and Prof. G. Kalmbach H.E. for her cordial hospitality and discussions.