Orderings of higher level in multifields and multirings
Abstract
In this note we generalize the concept of orderings of higher level to multifields and multirings. We show how part of the standard Artin-Schreier theory for orderings of higher level of fields and rings extends to multifields and multirings.
Keywords
multifields; multirings; orderings of higher level
References
2. Becker E., Gondard D., On rings admitting orderings and 2 -primary chains of orderings of higher level, Manuscripta Math. 65 (1989), 63–82.
3. Berr R., The intersection theorem for orderings of higher level in rings, Manuscripta Math. 75 (1992), 273–277.
4. Lam T.Y., The theory of ordered fields , in: B.R. McDonald, ed., Ring Theory and Algebra III, Lecture Notes in Pure and Appl. Math., vol. 55, Dekker, New York, 1980, pp. 1–152.
5. Marshall M., Real reduced multirings and multifields, J. Pure Appl. Algebra 205 (2006), 452–468.
6. Marshall M., Walter L., Signatures of higher level on rings with many units, Math. Z. 204 (1990), 129–143.
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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