States on pseudo-effect algebras with general comparability.
Anatolij Dvurečenskij · Czech digital mathematics library · 2004
ANATOLIJ DVURECENSKUPseudo-effect algebras are partial algebras (£?;+, 0,1) with a partially defined addition -I-which is not necessarily commutative and therefore with two complements, left and right ones.General comparability allows to compare elements of E in some intervals with Boolean ends.Such an algebra is always a pseudo MV-algebra.We show that it admits a state, and we describe the state space from the topological point of view.We prove that every pseudo-effect algebra is in fact a pseudo MV-algebra which is a subdirect product of linearly ordered pseudo-MV-algebras.In addition, we present many illustrating examples.