Abstract
The aim of this note is to study the ring\(\mathbb{Z} [\sqrt {14} ]\) and in particular the question whether it is Euclidean or not. The following results are obtained:
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1)
The couples of elements of\(\mathbb{Z} [\sqrt {14} ]\) which are not Euclidean with respect to the absolute value of the norm are determined.
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2)
An Euclidean algorithm for\(\mathbb{Z} [\sqrt {14} ]\) is constructed under suitable assumptions (Hypothèse 4.1).
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Bedocchi, E. L'anneau\(\mathbb{Z} [\sqrt {14} ]\) et l'algorithme Euclidien. Manuscripta Math 53, 199–216 (1985). https://doi.org/10.1007/BF01626396
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DOI: https://doi.org/10.1007/BF01626396