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Generalized orderings and rings of fractions
Authors:Jaka Cimprič  Igor Klep
Affiliation:(1) Oddelek za matematiko, Univerza v Ljubljani, FMF, Jadranska 19, SI-1111 Ljubljana, Slovenia;(2) Oddelek za matematiko Inštituta za matematiko, fiziko in mehaniko, Univerza v Ljubljani, Jadranska 19, SI-1111 Ljubljana, Slovenia
Abstract:Every total ordering of a commutative domain can be extended uniquely to its field of fractions. This result is extended in two directions. Firstly, the notion of a total ordering is generalized so that a nonzero element can have more than two signs (in fact, these signs form a group). Secondly, commutative domains are replaced by noncommutative ones and we consider the following types of rings of fractions: Ore extensions, maximal (right or two-sided) rings of fractions, division hulls of free algebras and epic fields. Throughout the paper several examples are given to illustrate the theory. Received January 8, 2005; accepted in final form November 1, 2005.
Keywords:14P99  13J25  16A06
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