The restricted Nagata’s pairwise algorithm and the Euclidean algorithm. (English) Zbl 1152.13016

Leu, Ming-Guang

Osaka J. Math. 45, No. 3, 807-818 (2008).

M. Nagata introduced [in: Algebraic geometry seminar. Proceedings of the seminar, Singapore, November 3–6, 1987. Singapore: World Scientific, 69–74 (1988; Zbl 0947.14500)] a generalization of the Euclidean algorithm. The author presents a modification of this algorithm, develops its properties and shows that if this algorithm exists in a ring of integers of a quadratic number field \(Q(\sqrt{-d})\), then \(d=1,2,3,7\) or \(11\).

Reviewer: Władysław Narkiewicz (Wrocław)

MSC:

13F07	Euclidean rings and generalizations
11R04	Algebraic numbers; rings of algebraic integers

Keywords:

Euclidean algorithm

Citations:

Zbl 0947.14500

References:

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