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\(p\)-integral bases of a cubic field. (English) Zbl 0908.11048

Let \(K\) be the cubic field generated by a root of a cubic polynomial \(f\). For each prime \(p\), the author constructs a \(p\)-integral basis (a basis with index prime to \(p\)) for the ring of integers in \(K\) in terms of the coefficients of \(f\), and then shows how to produce a global integral basis.
(Reviewer’s remark: The problem of constructing an explicit integral basis for cubic fields was solved by Voronoi [see B. Delone and D. Faddeev, The theory of irrationalities of the third degree, Translations Math. Monogr. 10 (1964; Zbl 0133.30202)]).

MSC:

11R04 Algebraic numbers; rings of algebraic integers
11R16 Cubic and quartic extensions

Citations:

Zbl 0133.30202
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