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Certain p-local orders in n-dimensional division algebras over the rational numbers occur as endomorphism rings of torsion-free abelian groups of rank n if and only if an associated finite poset P has a strict faithful representation of dimension less than |P| over the field with p elements. In this note we obtain a simple characterization of those finite posets which do not admit such a representation.
AMS subject classifications (1980)06A10 20K15 20K30
Key wordsPartially ordered set torsion-free abelian group
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