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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Hilbert's tenth problem for a class of rings of algebraic integers


Author: Thanases Pheidas
Journal: Proc. Amer. Math. Soc. 104 (1988), 611-620
MSC: Primary 12L05; Secondary 03C60, 03D35, 11U05
MathSciNet review: 962837
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Abstract: We show that $ {\mathbf{Z}}$ is diophantine over the ring of algebraic integers in any number field with exactly two nonreal embeddings into $ {\mathbf{C}}$ of degree $ \geq 3$ over $ {\mathbf{Q}}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0962837-4
Article copyright: © Copyright 1988 American Mathematical Society