Matematicky ustav SAV, Gresakova 6, 040 01 Kosice, Slovakia, e-mail: musavke@mail.saske.sk
Abstract: The distinguished completion $E(G)$ of a lattice ordered group $G$ was investigated by Ball [1], [2], [3]. An analogous notion for $MV$-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].
Keywords: lattice ordered group, distinguished completion, direct product
Classification (MSC 2000): 06F15
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