Linear extensions of partial orders on Abelian groups
mag(2011)
摘要
Partially ordered groups, also known as po-groups, are groups with a
compatible partial order. Results from M.I. Zajceva and H.-H. Teh are combined
in order to provide a full characterisation of linear order extensions of a
given order on a group. In contrast to Teh this approach provides a method to
discuss linear orders of different abelian rank in a uniform manner. This will
be achieved by modelling the linear orders using hyperplanes in a real vector
spaces. Among some additional remarks a construction of an archimedian directed
order is given for every torsion free abelian group.
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关键词
partial order,linear order,group theory,abelian group,vector space,linear extension
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