The Euclidean algorithm in algebraic number fields
This survey deals with the Euclidean algorithm and Euclidean minima in algebraic fields. Most work defines the Euclidean algorithm with respect to the norm function, but here other functions are also considered, as well as the \(k\)-stage algorithm first introduced by \textit{G. Cooke} [J. Reine Angew. Math. 282, 133-156 (1976; Zbl 0328.13013) and ibid. 283/284, 71-85 (1977; Zbl 0343.13008)]. Particular attention is paid to pointing out where unsolved problems exist and these are also shown by the gaps in the extensive tables of results. The bibliography contains 219 references, but unfortunately does not include all the papers cited in the survey, nor is it in strict alphabetical order, nor do the dates of papers always agree with the dates given in the survey. This is a pity, because it detracts a little from what is otherwise a valuable piece of work.
scientific article; zbMATH DE number 849120