| Résume | Hilbert's Theorem 90 gives a condition for an algebraic number\beta in a number field k to be a quotient $alpha/\alpha' ofconjugate algebraic numbers, for \alpha in a cyclic extensionL of k.In joint work with A. Dubickas, we find a simple necessary andsufficient condition for \beta\in k to be equal to\alpha/\alpha', where now $\alpha$ is unrestricted.Just as Hilbert's Theorem 90 has an additive version, so ourresult too has an additive analogue. |
