Undecidable existential problems for addition and divisibility in algebraic number rings. II
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- by Leonard Lipshitz PDF
- Proc. Amer. Math. Soc. 64 (1977), 122-128 Request permission
Abstract:
It is shown that for all algebraic number rings, except imaginary quadratic ones, the problem of deciding existential formulas involving only addition and the divisibility predicate is equivalent to the full diophantine problem for these rings.References
- A. I. Borevich and I. R. Shafarevich, Number theory, Pure and Applied Mathematics, Vol. 20, Academic Press, New York-London, 1966. Translated from the Russian by Newcomb Greenleaf. MR 0195803 R. D. Carmichael, On the numerical factors of the arithmetic forms ${\alpha ^n} \pm {\beta ^n}$, Ann. of Math. (2) 15 (1913).
- L. Lipshitz, The Diophantine problem for addition and divisibility, Trans. Amer. Math. Soc. 235 (1978), 271–283. MR 469886, DOI 10.1090/S0002-9947-1978-0469886-1
- L. Lipshitz, Undecidable existential problems for addition and divisibility in algebraic number rings, Trans. Amer. Math. Soc. 241 (1978), 121–128. MR 536658, DOI 10.1090/S0002-9947-1978-0536658-9
- Hermann Weyl, Algebraic Theory of Numbers, Annals of Mathematics Studies, No. 1, Princeton University Press, Princeton, N. J., 1940. MR 0002354
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 64 (1977), 122-128
- MSC: Primary 02E10; Secondary 02G05, 10N10
- DOI: https://doi.org/10.1090/S0002-9939-1977-0536659-5
- MathSciNet review: 0536659