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https://doi.org/10.1006/jabr.1994.1095
Title: | Strong Approximation Property for Baer Orderings on *-Fields | Authors: | Leung, K.H. | Issue Date: | 1-Apr-1994 | Citation: | Leung, K.H. (1994-04-01). Strong Approximation Property for Baer Orderings on *-Fields. Journal of Algebra 165 (1) : 1-22. ScholarBank@NUS Repository. https://doi.org/10.1006/jabr.1994.1095 | Abstract: | Let (D, *) be a *-field with [D: Z(D)] being finite. Our main objective is to show that the space of all Baer orderings (resp. weak *-orderings) of (D, *) satisfies the strong approximation property iff every Baer ordering of (D, *) is in fact a weak *-ordering. This shows that the notions of Baer orderings and weak *-orderings are respectively the "correct" analogues for semiorderings and orderings. We also intro-duce the concept of Baer formally real *-fields and Baer preorderings. We prove that a *-field admits a Baer ordering iff it is Baer formally real. In addition, some new results on weak *-orderings are also discussed. © 1994 Academic Press. All rights reserved. | Source Title: | Journal of Algebra | URI: | http://scholarbank.nus.edu.sg/handle/10635/104205 | ISSN: | 00218693 | DOI: | 10.1006/jabr.1994.1095 |
Appears in Collections: | Staff Publications |
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