Archimedean unital groups with finite unit intervals.

Foulis, David J.

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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 $ℓ$ -group. We present a connection among states and ideals of po-groups, and we describe extremal states on the state...