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arXiv · 1106.3938

Linear extensions of partial orders on Abelian groups

Tobias Schlemmer
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Abstract

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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Tobias Schlemmer. 2014-03-12. Linear extensions of partial orders on Abelian groups. https://arxiv.org/abs/1106.3938

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