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.
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Received January 8, 2005; accepted in final form November 1, 2005.
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Cimprič, J., Klep, I. Generalized orderings and rings of fractions. Algebra univers. 55, 93–109 (2006). https://doi.org/10.1007/s00012-006-1974-0
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DOI: https://doi.org/10.1007/s00012-006-1974-0