## $$p$$-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

Zbl 0133.30202
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