Generalized cardinal properties of lattices and lattice ordered groups

Ján Jakubík

Displaying similar documents to “Generalized cardinal properties of lattices and lattice ordered groups”

Distinguished completion of a direct product of lattice ordered groups

Ján Jakubík (2001)

Czechoslovak Mathematical Journal

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The distinguished completion $E (G)$ of a lattice ordered group $G$ was investigated by Ball [1], [2], [3]. An analogous notion for $M V$ -algebras was dealt with by the author [7]. In the present paper we prove that if a lattice ordered group $G$ is a direct product of lattice ordered groups $G_{i}$ $(i \in I)$ , then $E (G)$ is a direct product of the lattice ordered groups $E (G_{i})$ . From this we obtain a generalization of a result of Ball [3].

Weak homogeneity of lattice ordered groups

Ján Jakubík (2007)

Czechoslovak Mathematical Journal

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In this paper we deal with weakly homogeneous direct factors of lattice ordered groups. The main result concerns the case when the lattice ordered groups under consideration are archimedean, projectable and conditionally orthogonally complete.

On some interpolation rules for lattice ordered groups

Ján Jakubík (2004)

Czechoslovak Mathematical Journal

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Let $α$ be an infinite cardinal. In this paper we define an interpolation rule $I R (α)$ for lattice ordered groups. We denote by $C (α)$ the class of all lattice ordered groups satisfying $I R (α)$ , and prove that $C (α)$ is a radical class.