%0 Report %1 dd/MATH-AL-01-2011 %A Schlemmer, Tobias %C Dresden %D 2011 %K L-Gruppen myown Mathematik po-Gruppe Halbordnungen Preprint Ordnungen kommutativ tspub abelsche Gruppe %N MATH-AL-01-2011 %T Linear extensions of partial orders on Abelian groups %U http://arxiv.org/abs/1106.3938 %X 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 as hyperplanes in a real vector space.

@techreport{dd/MATH-AL-01-2011, 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 as hyperplanes in a real vector space.}, added-at = {2013-02-02T14:42:42.000+0100}, address = {Dresden}, author = {Schlemmer, Tobias}, bdsk-file-1 = {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}, biburl = {https://www.bibsonomy.org/bibtex/25bf71a481c57def61581d820df70f77c/ks-plugin-devel}, date-added = {2011-06-20 11:35:59 +0200}, date-modified = {2011-06-20 11:37:10 +0200}, file = {:linearization-preprint.pdf:PDF}, groups = {public}, institution = {Technische Universität Dresden}, interhash = {8576666d92bad283f7b1cb51576b82f1}, intrahash = {5bf71a481c57def61581d820df70f77c}, keywords = {L-Gruppen myown Mathematik po-Gruppe Halbordnungen Preprint Ordnungen kommutativ tspub abelsche Gruppe}, month = {June}, number = {MATH-AL-01-2011}, rating = {3}, read = {1}, timestamp = {2013-02-02T14:42:42.000+0100}, title = {Linear extensions of partial orders on Abelian groups}, type = {Preprint}, url = {http://arxiv.org/abs/1106.3938}, username = {keinstein}, year = 2011 }