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.
block pseudo-effect algebra pseudo effect algebra riesz interpolation property compatibility mv-algebra strong compatibility