# zbMATH — the first resource for mathematics

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
Full Text: