Chatelain's integer bases for biquadratic fields (Q2404137)

Integral bases of biquadratic fields of type \(\mathbb Q(\sqrt{m},\sqrt{n})\) was given by \textit{Y. Motoda} [Mem. Fac. Sci., Kyushu Univ., Ser. A 29, 263--268 (1975; Zbl 0314.12012)] and \textit{K. S. Williams} [Can. Math. Bull. 13, 519--526 (1970; Zbl 0205.35401)]. These results were extended to multiquadratic fields by \textit{B. Schmal} [Arch. Math. 52, No. 3, 245--257 (1989; Zbl 0684.12006)]. Monogenity of biquadratic fields was considered by \textit{M.-N. Gras} and \textit{F. Tanoé} [Manuscr. Math. 86, No. 1, 63--79 (1995; Zbl 0816.11058)] and \textit{I. Gaál} et al. [J. Number Theory 53, No. 1, 100--114 (1995; Zbl 0853.11026)]. Monogenity of certain orders of multiquadratic fields was studied by \textit{G. Nyul} [Acta Math. Inform. Univ. Ostrav. 10, No. 1, 85--93 (2002; Zbl 1058.11023)]. In the present paper the author goes back to a less known result of \textit{D. Chatelain} [Ann. Sci. Univ. Besançon, III. Sér., Math. 6, 38 p. (1973; Zbl 0289.12002)]. Using these results integral bases of biquadratic fields are constructed. These integral bases are explicit but rather complicated. Applying these bases the author considers monogeneity of biquadratic fields. The statements are formulated in terms of the solutions of the index form equation.