Undecidable existential problems for addition and divisibility in algebraic number rings-Reference-Cited by-同舟云学术

Undecidable existential problems for addition and divisibility in algebraic number rings

Published:1978 Issue:0 Volume:241 Page:121-128
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Lipshitz L.

Abstract

Existential formulas involving addition and divisibility are shown to be undecidable in the ring of integers of a real quadratic extension of the rationals. A weaker result is proved for extensions of higher degree.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1978-241-00/S0002-9947-1978-0536658-9/S0002-9947-1978-0536658-9.pdf

Reference5 articles.

1. A. P. Bel’tyukov, Abstracts: Students’ Scientific Conference, Leningrad University, 1975.

2. Pure and Applied Mathematics, Vol. 20;Borevich, A. I.,1966

3. On the numerical factors of the arithmetic forms 𝛼ⁿ±𝛽ⁿ;Carmichael, R. D.;Ann. of Math. (2),1913

4. Hilbert’s tenth problem for quadratic rings;Denef, J.;Proc. Amer. Math. Soc.,1975

5. The Diophantine problem for addition and divisibility;Lipshitz, L.;Trans. Amer. Math. Soc.,1978

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