Positive semidefinite forms over ordered skew fields

Author:
Ka Hin Leung

Journal:
Proc. Amer. Math. Soc. **106** (1989), 933-942

MSC:
Primary 11E76; Secondary 11E81, 12J15, 16A39, 16A70, 16A86

DOI:
https://doi.org/10.1090/S0002-9939-1989-0976367-8

MathSciNet review:
976367

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Abstract: In any ordered field , the inequality obviously holds for any . Naturally, we may ask if the same inequality holds in every ordered skew field. Surprisingly, it can be proved that in an ordered domain , the above inequality holds for any elements in iff is commutative. In this paper, we formulate a generalization of the above observation and prove that if a "positive semidefinite form" over an ordered skew field admits a "nontrivial" solution, then the skew field is actually a field.

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DOI:
https://doi.org/10.1090/S0002-9939-1989-0976367-8

Article copyright:
© Copyright 1989
American Mathematical Society