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We give two variations of the Holland representation theorem for -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 -algebra can be represented as a pseudo-effect algebra or as a pseudo -algebra of automorphisms of some antilattice or of some linearly ordered set.
We study states on unital po-groups which are not necessarily commutative as normalized positive real-valued group homomorphisms. We show that in contrast to the commutative case, there are examples of unital po-groups having no state. We introduce the state interpolation property holding in any Abelian unital po-group, and we show that it holds in any normal-valued unital -group. We present a connection among states and ideals of po-groups, and we describe extremal states on the state space of...
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