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

Pheidas, Thanases

doi:10.1090/S0002-9939-1988-0962837-4

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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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