Blocks of pseudo-effect algebras with the Riesz interpolation property

Abstract

 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.