Pseudoeffect (PE-) algebras are partial additive structures
differing from effect algebras in no longer being necessarily
commutative. PE-algebras typically arise from intervals of \pogr{}s;
this applies in particular to all those which fulfil a certain Riesz
property.

In this paper, we discuss the property of archimedeaness for
PE-algebras on the one hand and for \pogr{}s on the other hand. We
prove that under the assumption of supremum-homogenicity,
archimedeaness holds for a PE-algebra with Riesz property if and
only if it holds for its representing group. The algebra is in that
case commutative.

This result is established by using the technique of MacNeille
completion. We give the exact condition for this completion to
exist, and we clearly exhibit the role played by archimedeaness and
by supremum-homogenicity.
