Pseudoeffect (PE-) algebras generalize effect algebras by no longer
being necessarily commutative. They are in certain cases
representable as the unit interval of a unital \pogr{}, for instance
if they fulfil a certain Riesz property.

Several infinitary lattice properties and the countable Riesz
interpolation property are studied for PE-algebras on the one hand
and for \pogr{}s on the other hand. We establish the exact
relationships between the various conditions that are taken into
account, and in particular, we examine how properties of a
PE-algebra are related to the analogous properties of a representing
\pogr{}.
