Free generating sets of lattice-ordered abelian groups

doi:10.1016/j.jpaa.2007.03.002

Journal of Pure and Applied Algebra

Volume 211, Issue 2, November 2007, Pages 400-403

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Abstract

We prove that the generators $g_{1}, \dots, g_{n}$ of a lattice-ordered abelian group $G$ form a free generating set iff each $ℓ$ -ideal generated by any $n - 1$ linear combinations of the $g_{i}$ is strictly contained in some maximal $ℓ$ -ideal of $G$ .

MSC

Primary

06F20

secondary

08B20