Holland’s theorem for pseudo-effect algebras
Anatolij Dvurečenskij · Czechoslovak Mathematical Journal · 2006
We give two variations of the Holland representation theorem for ℓ-groups and of its generalization of Glass for directed interpolation po-groups as groups of automorphisms of a linearly ordered set or of an antilattice, respectively. We show that every pseudo-effect algebra with some kind of the Riesz decomposition property as well as any pseudo MV -algebra can be represented as a pseudo-effect algebra or as a pseudo MV -algebra of automorphisms of some antilattice or of some linearly ordered set.