Linear extensions of partial orders on Abelian groups
Group Theory
2014-03-13 v5
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.
Cite
@article{arxiv.1106.3938,
title = {Linear extensions of partial orders on Abelian groups},
author = {Tobias Schlemmer},
journal= {arXiv preprint arXiv:1106.3938},
year = {2014}
}
Comments
Talk at AAA81 conference in Salzburg. Completely revised version. revised version of: Technische Universti\"at Preprint MATH-AL-01-2011