2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166964Let $E/F$ be a cyclic Galois extension of degree $p^l$ with Galois group $G$. It is shown that the Galois module structure of both sides of the Kummer pairing (for Kummer extensions of $E$) are the same. In other words, we show that the Kummer duality holds in the level of finitely generated $G$-modules.6 pagesNumber Theorytext