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Hilbert’s tenth problem for a class of rings of algebraic integers. (English) Zbl 0697.12020
The author shows that \({\mathbb{Z}}\) is diophantine over the ring of algebraic integers in any number field with exactly two nonreal embeddings into \({\mathbb{C}}\) of degree \(\geq 3\) over \({\mathbb{Q}}\).
Reviewer: D.Busneag

MSC:
12L05 Decidability and field theory
11D99 Diophantine equations
03B25 Decidability of theories and sets of sentences
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