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References
Artin, E. and Schreier, O.: Algebraische Konstruktion reeller Körper, Abh. Math. Sem. Univ. Hamburg 5 (1927), 85–99.
Baer, R.: Über nicht-archimedisch geordnete Körper, Sitz. Ber. der Heidelberger Akad., 8. Abh. (1927), 3–13.
Becker, E.: Hereditarily pythagorean fields and orderings of higher level. IMPA Lecture Notes, No. 29 (1978), Rio de Janeiro.
Becker, E.: Summen n-ter Potenzen in Körpern, J. reine angew. Mathematik 307/308 (1979), 8–30.
Becker, E.: Partial orders on a field and valuation rings, Comm. Alg. 7 (1979), 1933–1976.
Becker, E.: Local global theorems for diagonal forms of higher degree, J. reine angew. Math. 318 (1980), 36–50.
Becker, E.: The real holomorphy ring and sums of 2n-th powers, these Proceedings.
Becker, E. and Bröcker, L.: On the description of the reduced Witt ring, J. Alg. 52 (1978), 328–346.
Becker, E. and Köpping, E.: Reduzierte quadratische Formen und Semiordnungen reeller Körper, Abh. Math. Sem. Univ. Hamburg 46 (1977), 143–177.
Bröcker, L.: Zur Theorie der quadratischen Formen über formal reellen Körpern, Math. Ann. 210 (1974), 233–256.
Bröcker, L.: Characterization of fans and hereditarily pythagorean fields, Math. Z. 151 (1976), 149–163.
Brown, R. and Marshall, M.: The reduced theory of quadratic forms, Rocky Mtn. J. Math. 11 (1981), 161–175.
Brumfiel, G.: Partially ordered rings and semi-algebraic geometry, Lect. Notes Ser. Lond. Math. Soc. 1979.
Cassels, J.W.S. and Ellison, W.J. and Pfister, A.: On sums of squares and on elliptic curves over function fields, J. Numb. Th. 3 (1971), 125–149.
Chevalley, C.: Introduction to the theory of algebraic functions of one variable, Math. Surveys VI of the Amer. Math. Soc. 1951.
Dress, A.: On orderings and valuation of fields, Geometriae Ded. 6 (1977), 259–266.
Dubois, D.W.: A note on David Harrison’s theory of preprimes, Pac. J. Math. 21 (1967), 15–19.
Dubois, D.W.: Second note on David Harrison’s theory of preprimes, Pac. J. Math. 24 (1968), 57–68.
Dubois, D.W.: Infinite primes and ordered fields, Diss. Math. LXIX (1970).
Dubois, D.W.: Real commutative algebra I. Places, Revista Matemática Hispana-Americana 39 (1979), 57–65.
Dubois, D.W. and Efroymson, G.: Algebraic theory of real varieties, "Studies and Essays" presented to Yu-Why Chen on his 60th birthday (1970), 107–135.
Gilmer, R.: Multiplicative ideal theory, New York 1972.
Grothendieck, A.: Eléments de géométrie algébrique, Publ. Math. IHES 20 (1964).
Joly, J.R.: Sommes des puissances d-ièmes dans un anneau commutatif, Acta Arith. 17 (1970), 37–114.
Kadison, R.V.: A representation theorem for commutative topological algebra, Mem. Amer. Math. Soc. 7 (1951).
Knebusch, M.: Specialization of quadratic and symmetric bilinear forms, and a norm theorem, Acta Arith. 24 (1973), 279–299.
Lam, T.Y.: The algebraic theory of quadratic forms, Reading 1973.
Lang, S.: Algebra, Reading 1965.
Marshall, M.: Abstract Witt rings, Queen’s Paper in Pure and Applied Mathematics 57 (1980), Kingston.
Pfister, A.: Quadratische Formen in beliebigen Körpern, Invent. Math. 1 (1966), 116–132.
Prestel, A.: Quadratische Semi-Ordnungen und quadratische Formen, Math. Z. 133 (1973), 319–342.
Prestel, A.: Lectures on formally real fields, IMPA Lecture Notes No. 22 (1975), Rio de Janeiro.
Siegel, C.L.: Darstellung total positiver Zahlen durch Quadrate, Math. Z. 11 (1921), 246–275.
Schülting, H.-W.: Über reelle Stellen eines Körpers und ihren Holomorphiering, Ph.D. thesis, Dortmund 1979.
Schülting, H.-W.: On real places of a field and their holomorphy ring, Comm. Alg., to appear.
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Becker, E. (1982). Valuations and real places in the theory of formally real fields. In: Colliot-Thélène, JL., Coste, M., Mahé, L., Roy, MF. (eds) Géométrie Algébrique Réelle et Formes Quadratiques. Lecture Notes in Mathematics, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062248
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