, Volume 7, Issue 3, pp 275–282 | Cite as

Realizable posets

  • R. S. Pierce
  • C. Vinsonhaler


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 words

Partially ordered set torsion-free abelian group 


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  1. 1.
    R. P.Dilworth (1960) A decomposition theorem for partially ordered sets, Ann. of Math. 51, 161–166.Google Scholar
  2. 2.
    R. S. Pierce and C. Vinsonhaler (19XX) Realizing tiled orders, preprint.Google Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • R. S. Pierce
    • 1
  • C. Vinsonhaler
    • 2
  1. 1.Department of MathematicsUniversity of ArizonaTucsonUSA
  2. 2.Department of MathematicsUniversity of ConnecticutStorrsUSA

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