On a relative uniform completion of an Archimedean lattice ordered group

Year, pages: 2009, 231 - 250

The notion of a relatively uniform convergence ($\ru$-convergence) has been used first in vector lattices and then in Archimedean lattice ordered groups. Let $G$ be an Archimedean lattice ordered group. In the present paper, a relative uniform completion ($\ru$-completion) $G_ω1$ of $G$ is dealt with. It is known that $G_ω1$ exists and it is uniquely determined up to isomorphisms over $G$. The $\ru$-completion of a finite direct product and of a completely subdirect product are established. We examine also whether certain properties of $G$ remain valid in $G_ω1$. Finally, we are interested in the existence of a greatest convex $l$-subgroup of $G$, which is complete with respect to $\ru$-convergence.

Černák, Š., Lihová, J. 2009. On a relative uniform completion of an Archimedean lattice ordered group. In Mathematica Slovaca, vol. 59, no.2, pp. 231-250. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0120-9

Černák, Š., Lihová, J. (2009). On a relative uniform completion of an Archimedean lattice ordered group. Mathematica Slovaca, 59(2), 231-250. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0120-9