×
Becker, Eberhard; Köpping, Eberhard

Reduzierte quadratische Formen und Semiordnungen reeller Körper. (German) Zbl 0365.12011

Abh. Math. Semin. Univ. Hamb. 46, 143-177 (1977).
Reviewer: D. B. Shapiro
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0365.12011

Cited in 3 Reviews
Cited in 24 Documents

MSC:

12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
11E04 Quadratic forms over general fields
11E81 Algebraic theory of quadratic forms; Witt groups and rings

Keywords:

reduced quadratic forms; semiorderings of real fields

Citations:

Zbl 0273.13018; Zbl 0275.12013; Zbl 0548.12010; Zbl 0548.12011; Zbl 0281.10012; Zbl 0348.15015; Zbl 0319.12012; Zbl 0396.10012
PDF BibTeX XML Cite
\textit{E. Becker} and \textit{E. Köpping}, Abh. Math. Semin. Univ. Hamb. 46, 143--177 (1977; Zbl 0365.12011)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Arason, J. K. undPfister, A.: Beweis des Krullschen Durchschnittsatzes für den Wittring, Invent. Math. 12 (1971), 173–176. · Zbl 0212.37302
[2] Becker, E.: Euklidische Körper und euklidische Hüllen von Körpern. J. reine angew. Math. 268 (1974), 41–52. · Zbl 0289.12103
[3] Bourbaki, N.: Groupes et corps ordonné, Algèbre, Chap. VI, Paris 1952. · Zbl 0049.01801
[4] Bröcker, L.: Eine Bemerkung zu den Wittringen endlicher galoisscher Körperwerweiterungen, Math. Ann. 192 (1971), 250–252. · Zbl 0214.29701
[5] Bröcker, L.: Über eine Klasse pythgoreischer körper, Arch. der Math. 23 (1972), 405–407. · Zbl 0251.12102
[6] Bröcker, L.: Zur Theorie der quadratischen Formen über formal-reellen Körpern, erscheint demnächst. · Zbl 0273.13018
[7] Crayen, T. C.: The topological space of orderings of a rational function field, Duke Math. J., erscheint demnächst.
[8] Diller, J. undDress, A.: Zur Galoistheorie pythagoreischer Körper, Arch. der Math. 16 (1965), 148–152. · Zbl 0136.25106
[9] Elman, R. andLam, T. Y.: Quadratic forms over formally real fields and pythagorean fields, Amer. J. Math. 94 (1972), 1155–1194. · Zbl 0259.12101
[10] Elman, R. andLam, T. Y.: Pfister forms and K-Theory of fields, J. Algebra 23 (1972), 181–213. · Zbl 0246.15029
[11] Elman, R., Lam, T. Y. andPrestel, A.: On some Hasse principles over formally real fields, Math. Z. 134 (1973), 291–301. · Zbl 0277.15013
[12] Harrison, D. K.: Witt rings, Lecture notes, Departments of Mathematics, University of Kentucky, Lexington, Kentucky, 1970.
[13] Hsia, J. S. andJohnson, R. P.: Round and group quadratic forms over global fields, J. of number Theory 5 (1973) 356–366. · Zbl 0266.10020
[14] Hsia, J. S. andJohnson, R. P.: Round and Pfister forms overR(t) Pac. J. Math. 49 (1973), 101–108.
[15] Knebusch, M.: Runde Formen über semilokalen Ringen, Math. Ann. 93 (1971), 21–24. · Zbl 0217.04701
[16] Knebusch, M.: Generalization of a theorem of Artin-Pfister to arbitrary semilocal rings, and related topics, erscheint demnächst. · Zbl 0315.13014
[17] Knebusch, M., Rosenberg, A. andWare, R.: Structure of Witt rings and quotients of abelian group rings, Amer. J. Math 94 (1972), 119–155. · Zbl 0248.13030
[18] Knebusch, M., Rosenberg, A. andWare, R.: Signatures on semilocal rings, J. of Algebra 26 (1973), 208–250. · Zbl 0273.13016
[19] Lam, T. Y.: The algebraic theory of quadratic forms, Reading 1973. · Zbl 0259.10019
[20] Lorenz, F.: Quadratische Formen über Körpern Lecture Notes in Mathematics, 130, Berlin-Heidelberg-New York 1970. · Zbl 0211.35303
[21] Pfister, A.: Quadratische Formen in beliebigen Körpern, Invent. Math 1 (1966), 116–132. · Zbl 0142.27203
[22] Prestel, A.: Quadratische Semi-Ordnungen und quadratische Formen, Math. Z. 133 (1973), 319–342. · Zbl 0275.12013
[23] Prestel, A. undZiegler, M.: Erblich euklidische Körper, J. reine angew. Math., erscheint demnächst.
[24] Scharlau, W.: Quadratic forms, Queen’s papers on pure and applied mathematics, 22, Kingston, Ontario (1969). · Zbl 0194.35104
[25] Ware, R.: When are Witt rings group rings? Pac. J. of Math. 49 (1973), 279–284. · Zbl 0302.13018
[26] Witt, E.: Theorie der quadratischen Formen in beliebigen Körpern, J. reine angew. Math. 176 (1937), 31–44. · Zbl 0015.05701
[27] Dress, A.: Trägheitsstrukturen quadratischer Formen, Math. Annalen 157 (1964), 326–331. · Zbl 0132.25701
[28] Knebusch, M.: Spezialization of quadratic and symmetric bilinear forms, and a norm theorem, Acta Arithmetica 24 (1973), 279–299. · Zbl 0287.15010
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.