Displaying similar documents to “States on unital partially-ordered groups”

Holland’s theorem for pseudo-effect algebras

Anatolij Dvurečenskij (2006)

Czechoslovak Mathematical Journal

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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 M V -algebra can be represented as a pseudo-effect algebra or as a pseudo M V -algebra of automorphisms of some antilattice or of some linearly ordered...

Generalizations of pseudo MV-algebras and generalized pseudo effect algebras

Jan Kühr (2008)

Czechoslovak Mathematical Journal

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We deal with unbounded dually residuated lattices that generalize pseudo M V -algebras in such a way that every principal order-ideal is a pseudo M V -algebra. We describe the connections of these generalized pseudo M V -algebras to generalized pseudo effect algebras, which allows us to represent every generalized pseudo M V -algebra A by means of the positive cone of a suitable ℓ -group G A . We prove that the lattice of all (normal) ideals of A and the lattice of all (normal) convex ℓ -subgroups of...