Geodesic
The Real Spectrum of Higher Level of a Commutative Ring
Canadian journal of mathematics, Tome 44 (1992) no. 3, pp. 449-462

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-1992-029-8
Mots-clés : 13, 06 
The Real Spectrum of Higher Level of a Commutative Ring. Canadian journal of mathematics, Tome 44 (1992) no. 3, pp. 449-462. doi: 10.4153/CJM-1992-029-8
@misc{10_4153_CJM_1992_029_8,
     title = {The {Real} {Spectrum} of {Higher} {Level} of a {Commutative} {Ring}},
     journal = {Canadian journal of mathematics},
     pages = {449--462},
     year = {1992},
     volume = {44},
     number = {3},
     doi = {10.4153/CJM-1992-029-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1992-029-8/}
}
TY  - JOUR
TI  - The Real Spectrum of Higher Level of a Commutative Ring
JO  - Canadian journal of mathematics
PY  - 1992
SP  - 449
EP  - 462
VL  - 44
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1992-029-8/
DO  - 10.4153/CJM-1992-029-8
ID  - 10_4153_CJM_1992_029_8
ER  - 
%0 Journal Article
%T The Real Spectrum of Higher Level of a Commutative Ring
%J Canadian journal of mathematics
%D 1992
%P 449-462
%V 44
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1992-029-8/
%R 10.4153/CJM-1992-029-8
%F 10_4153_CJM_1992_029_8

[1] 1. Artin, E. and Schreier, O., Algebraische Konstruktion reeller Korper, Abh. Math. Sem. Univ. Hamburg 5 (1927),85–99. Google Scholar

[2] 2. Artin, E. and Schreier, O., Eine Kennzeichnung der reell abgeschlossen Korper. Abh. Math. Sem. Univ. Hamburg 5 (1927), 225–231. Google Scholar

[3] 3. Baer, R., Über nicht-archimedisch geordnete Korper, Sitz. Ber. der Heidelberger Akad. Abh. (1927), 3–13. Google Scholar

[4] 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] 5. Becker, E., Summen n-ter Potenzen in Körpern, J. Reine Angew. Math. 307/308 (1979), 8–30. Google Scholar

[6] 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] 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] 8. Becker, E. and Rosenberg, A., Reduced forms and reduced Witt rings of higher level, J. Algebra 92 (1985), 477–503. Google Scholar

[9] 9. Berr, R., Réelle algebraische Géométrie hôhererStufe. Dissertation, Univ. Miinchen, Fed. Rep. of Germany, 1988. Google Scholar

[10] 10. Carrai, M. and Coste, M., Normal spectral spaces and their dimensions, J. Pure Appl. Alg. 30 (1983), 227- 235. Google Scholar

[11] 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] 12. Hochster, M., Prime ideal structure in commutative rings, Trans. AMS 142 (1969), 43–60. Google Scholar

[13] 13. Johnstone, P.T., Stone spaces. Cambridge Univ. Press, Cambridge, 1982. Google Scholar

[14] 14. Kelley, J.L., General topology. Van Nostrand Reinhold Company, New York, 1955. Google Scholar

Cité par Sources :