We prove that the generators g1, ..., gn 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 gi is strictly contained in some maximal ℓ-ideal of G.
Free generating sets of lattice-ordered abelian groups / D. MUNDICI. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - STAMPA. - 211:(2007), pp. 400-403. [10.1016/j.jpaa.2007.03.002]
Free generating sets of lattice-ordered abelian groups
MUNDICI, DANIELE
2007
Abstract
We prove that the generators g1, ..., gn 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 gi is strictly contained in some maximal ℓ-ideal of G.
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