caa a22 4500 467899517 CHVBK 20180406152813.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s00012-006-1974-0 doi (NATIONALLICENCE)springer-10.1007/s00012-006-1974-0 Generalized orderings and rings of fractions [Elektronische Daten] [Jaka Cimprič, Igor Klep] 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. Birkhäuser Verlag, Basel, 2006 Ordered rings nationallicence orderings of higher level nationallicence rings of fractions nationallicence free rings nationallicence free fields nationallicence Cimprič Jaka Oddelek za matematiko, Univerza v Ljubljani, FMF, Jadranska 19, SI-1111, Ljubljana, Slovenia aut Klep Igor Oddelek za matematiko Inštituta za matematiko, fiziko in mehaniko, Univerza v Ljubljani, Jadranska 19, SI-1111, Ljubljana, Slovenia aut algebra universalis Birkhäuser-Verlag; www.birkhauser.ch 55/1(2006-01-01), 93-109 0002-5240 55:1<93 2006 55 12 https://doi.org/10.1007/s00012-006-1974-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00012-006-1974-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cimprič Jaka Oddelek za matematiko, Univerza v Ljubljani, FMF, Jadranska 19, SI-1111, Ljubljana, Slovenia aut NATIONALLICENCE 700 1- Klep Igor Oddelek za matematiko Inštituta za matematiko, fiziko in mehaniko, Univerza v Ljubljani, Jadranska 19, SI-1111, Ljubljana, Slovenia aut NATIONALLICENCE 773 0- algebra universalis Birkhäuser-Verlag; www.birkhauser.ch 55/1(2006-01-01), 93-109 0002-5240 55:1<93 2006 55 12 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer