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Bulletin of the American Mathematical Society

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Hereditarily pythagorean fields, infinite Harrison-primes and sums of $2^n$th powers


Author: Eberhard Becker
Journal: Bull. Amer. Math. Soc. 84 (1978), 278-280
MSC (1970): Primary 12D15, 12E99
DOI: https://doi.org/10.1090/S0002-9904-1978-14474-7
MathSciNet review: 0460295
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  • 1. Eberhard Becker, Valuations and real places in the theory of formally real fields, Real algebraic geometry and quadratic forms (Rennes, 1981) Lecture Notes in Math., vol. 959, Springer, Berlin-New York, 1982, pp. 1–40. MR 683127
  • 2. L. Bröcker, Characterization of fans and hereditarily pythagorean fields, Math. Z. 151 (1976), 149-163. MR 422233
  • 3. W. D. Geyer, Unendliche algebraische Zahlkörper, über denen jede Gleichung auflösbar von beschränkter Stufe ist, J. Number Theory 1 (1969), 346-374. MR 282946
  • 4. D. K. Harrison, Finite and infinite primes for rings and fields, Mem. Amer. Math. Soc. 68 (1966), 1-62. MR 207735
  • 5. D. K. Harrison and H. Warner, Infinite primes of fields and completions, Pacific J. Math. 45 (1973), 201-216. MR 379456
  • 6. David Hilbert, Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl 𝑛^{𝑡𝑒𝑟} Potenzen (Waringsches Problem), Math. Ann. 67 (1909), no. 3, 281–300 (German). MR 1511530, https://doi.org/10.1007/BF01450405
  • 7. J.-R. Joly, Sommes des puissances d-ièmes dans un anneau commutatif, Acta Arith. 17 (1970), 37-114. MR 263779

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DOI: https://doi.org/10.1090/S0002-9904-1978-14474-7

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