Alaca, Saban \(p\)-integral bases of a cubic field. (English) Zbl 0908.11048 Proc. Am. Math. Soc. 126, No. 7, 1949-1953 (1998). 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)]). Reviewer: Franz Lemmermeyer (Bonn) Cited in 3 ReviewsCited in 10 Documents MSC: 11R04 Algebraic numbers; rings of algebraic integers 11R16 Cubic and quartic extensions Keywords:Voronoi’s theory; algorithm; integral basis of cubic field Citations:Zbl 0133.30202 × Cite Format Result Cite Review PDF Full Text: DOI