We characterize the Lebesgue state of a free finitely generated unital lattice-ordered abelian group G in terms of its value at each element of each basis of G. This significantly strengthens one of the main results of our previous paper (co-authored by D. Mundici) with the same title as the present one. As a consequence of independent interest, we obtain a state-theoretic characterization of free finitely generated objects in the category of unital lattice-ordered abelian groups and their unit-preserving lattice-group homomorphisms.
The Lebesgue state of a unital Abelian lattice-ordered group, II / V. Marra. - In: JOURNAL OF GROUP THEORY. - ISSN 1433-5883. - 12:6(2009 Nov), pp. 911-922.
The Lebesgue state of a unital Abelian lattice-ordered group, II
V. MarraPrimo
2009
Abstract
We characterize the Lebesgue state of a free finitely generated unital lattice-ordered abelian group G in terms of its value at each element of each basis of G. This significantly strengthens one of the main results of our previous paper (co-authored by D. Mundici) with the same title as the present one. As a consequence of independent interest, we obtain a state-theoretic characterization of free finitely generated objects in the category of unital lattice-ordered abelian groups and their unit-preserving lattice-group homomorphisms.Pubblicazioni consigliate
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