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Transactions of the American Mathematical Society

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Undecidable existential problems for addition and divisibility in algebraic number rings

Author: L. Lipshitz
Journal: Trans. Amer. Math. Soc. 241 (1978), 121-128
MSC: Primary 02E10; Secondary 02G05, 10N10
MathSciNet review: 0536658
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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.

References [Enhancements On Off] (What's this?)

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  • [3] R. D. Carmichael, On the numerical factors of the arithmetical forms $ {\alpha ^n} + {\beta ^n}$, Ann. of Math. (2) 15 (1913), 30-70. MR 1502458
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Article copyright: © Copyright 1978 American Mathematical Society

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