Displaying similar documents to “Generalizations of pseudo MV-algebras and generalized pseudo effect algebras”

On varieties of pseudo M V -algebras

Ján Jakubík (2003)

Czechoslovak Mathematical Journal

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In this paper we investigate the relation between the lattice of varieties of pseudo M V -algebras and the lattice of varieties of lattice ordered groups.

Convex chains in a pseudo MV-algebra

Ján Jakubík (2003)

Czechoslovak Mathematical Journal

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For a pseudo M V -algebra 𝒜 we denote by ℓ ( 𝒜 ) the underlying lattice of 𝒜 . In the present paper we investigate the algebraic properties of maximal convex chains in ℓ ( 𝒜 ) containing the element 0. We generalize a result of Dvurečenskij and Pulmannová.

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...