Chatelain’s integer bases for biquadratic fields

Abstract

Let \(K=\mathbb {Q}(\sqrt{dm}, \sqrt{dn})\) be a biquadratic field. In this paper we give a new integral basis for \(\mathbb {Z}_{K}\), by applying to biquadratic fields a method of D. Chatelain, for building formel integral bases of n-quadratic fields’ ring of integers. We give some examples. We set the monogenesis problem’s equations, and find the same characterizations that we’ve found, when we had used other bases. We give also new expressions for the elements of monogenesis.