Realizable posets |
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| Authors: | R S Pierce C Vinsonhaler |
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| Institution: | (1) Department of Mathematics, University of Arizona, 85721 Tucson, AZ, USA;(2) Department of Mathematics, University of Connecticut, 06268 Storrs, CT, USA |
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| Abstract: | 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.Research supported in part by NSF grant DMS-8802833. |
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| Keywords: | 06A10 20K15 20K30 |
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