Value quotients and product torsion classes of lattice-ordered groups

• Autores: Michael R. Darnel
• Localización: Algebra universalis, ISSN 0002-5240, Vol. 60, Nº. 4, 2009, págs. 405-423
• Idioma: inglés
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• Resumen

  • For a set X of archimedean o-groups, the class $${\mathcal{VQ}}(X) $$ of normal-valued l-groups having the property that every value quotient is in X is a complete torsion class. A question of Conrad whether the class $${\mathcal{VQ}}({\mathbb{R}})$$ is a product torsion class is partially answered by investigating values and value quotients of products of normal-valued l-groups. A major result is that the conjecture that all outer value quotients must be Dedekind complete is equivalent to the conjecture that measurable cardinals do not exist.