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The undecidability of algebraic rings and fields. (English) Zbl 0100.01501


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[1] Emil Artin, Lectures on modern higher algebra, Part III, mimeographed notes, New York University, 1948.
[2] Ph. Furtwängler, Die Reziprozitätsgesetze für Potenzreste mit Primzahlexponenten in algebraischen Zahlkörpern, Math. Ann. 74 (1913), no. 3, 413 – 429 (German). · doi:10.1007/BF01456752
[3] Helmut Hasse, Kurt Hensels entscheidender Anstoss zur Entdeckung des Lokal-Global-Prinzips, J. Reine Angew. Math. 209 (1962), 3 – 4 (German). · Zbl 0199.09804 · doi:10.1515/crll.1962.209.3
[4] -, Darstellbarkeit von Zahlen durch quadratische Formen in einem beliebigen algebraischen Zahlkörper, J. Reine Angew. Math. vol. 153 (1923) pp. 113-130.
[5] -, Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper, Teil I, Jahresbericht der Deutschen Mathematiker-Vereinigung vol. 35 (1926) pp. 1-55.
[6] Julia Robinson, Definability and decision problems in arithmetic, J. Symbolic Logic 14 (1949), 98 – 114. · Zbl 0034.00801 · doi:10.2307/2266510
[7] Raphael M. Robinson, Undecidable rings, Trans. Amer. Math. Soc. 70 (1951), 137 – 159. · Zbl 0042.24503
[8] Raphael M. Robinson, Arithmetical definability of field elements, J. Symbolic Logic 16 (1951), 125 – 126. · Zbl 0042.24601 · doi:10.2307/2266685
[9] Alfred Tarski, Undecidable theories, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam, 1953. In collaboration with Andrzej Mostowski and Raphael M. Robinson. · Zbl 0053.00401
[10] Ernst Witt, Theorie der quadratischen Formen in beliebigen Körpern, J. Reine Angew. Math. vol. 176 (1936) pp. 31-44. · Zbl 0015.05701
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