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The Real Spectrum of Higher Level of a Commutative Ring

Published online by Cambridge University Press:  20 November 2018

Susan Maureen Barton
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Abstract

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The following paper defines a new type of ordering of higher level on a commutative ring. This definition allows the set of all orderings of level n to be given a topology which we show is consistent with the topology of the real spectrum.

Keywords

1306
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 3 , 01 June 1992 , pp. 449 - 462
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Artin, E. and Schreier, O., Algebraische Konstruktion reeller Korper, Abh. Math. Sem. Univ. Hamburg 5 (1927),85–99.Google Scholar
2. Artin, E. and Schreier, O., Eine Kennzeichnung der reell abgeschlossen Korper. Abh. Math. Sem. Univ. Hamburg 5 (1927), 225–231.Google Scholar
3. Baer, R., Über nicht-archimedisch geordnete Korper, Sitz. Ber. der Heidelberger Akad. Abh. (1927), 3–13.Google Scholar
4. Becker, E., On the real spectrum of a ring and its applications to semialgebraic geometry. Bull. Amer. Math. Soc. (N.S.) 15 (1986), 19–60.Google Scholar
5. Becker, E., Summen n-ter Potenzen in Körpern, J. Reine Angew. Math. 307/308 (1979), 8–30.Google Scholar
6. Becker, E., and Gondard, D., On rings admitting orderings and 2-primary chains of orderings of higher level, Manuscripta Math. 65 (1989), 63–82.Google Scholar
7. Becker, E., Harman, J. and Rosenberg, A., Signatures of fields and extension theory, J. Reine Angew. Math. 330 (1982), 53–75.Google Scholar
8. Becker, E. and Rosenberg, A., Reduced forms and reduced Witt rings of higher level, J. Algebra 92 (1985), 477–503.Google Scholar
9. Berr, R., Réelle algebraische Géométrie hôhererStufe. Dissertation, Univ. Miinchen, Fed. Rep. of Germany, 1988.Google Scholar
10. Carrai, M. and Coste, M., Normal spectral spaces and their dimensions, J. Pure Appl. Alg. 30 (1983), 227- 235.Google Scholar
11. Coste, M. and Coste-Roy, M.-F., La topologie du spectre reel, Ordered fields and real algebraic geometry (Dubois, D. and Reico, T., éd.), Contemporary Math. 8, Amer. Math. Soc, Providence, R.I. (1982), 27–59.Google Scholar
12. Hochster, M., Prime ideal structure in commutative rings, Trans. AMS 142 (1969), 43–60.Google Scholar
13. Johnstone, P.T., Stone spaces. Cambridge Univ. Press, Cambridge, 1982.Google Scholar
14. Kelley, J.L., General topology. Van Nostrand Reinhold Company, New York, 1955.Google Scholar