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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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
DOI: https://doi.org/10.1090/S0002-9947-1978-0536658-9
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.


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DOI: https://doi.org/10.1090/S0002-9947-1978-0536658-9
Article copyright: © Copyright 1978 American Mathematical Society