Electronic Resource
Springer
Manuscripta mathematica
44 (1983), S. 109-130
ISSN:
1432-1785
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We are concerned with the following problem. Given a ring R and an epic R-field K, under what conditions can K be fully ordered? Epic R-fields can be constructed in terms of matrices over R; this makes it natural to consider matrix cones over R rather than ordinary cones of elements of K. Essentially, a matrix cone over R, associated with a given ordering of K, consists of all square matrices which either become singular or have positive Dieudonné determinant over K. We give necessary and sufficient conditions in terms of matrix cones for (i) an epic R-field to be orderable, (ii) a full order on R to be extendable to a field of fractions of R and (iii) for such an extension to be unique.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01166078
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