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Realizable posets

✍ Scribed by R. S. Pierce; C. Vinsonhaler

Publisher: Springer Netherlands
Year: 1990
Tongue: English
Weight: 494 KB
Volume: 7
Category: Article
ISSN: 0167-8094
DOI: 10.1007/bf00418655

No coin nor oath required. For personal study only.

✦ Synopsis

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 [Pi 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.

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