Arithmetic of interior extensions

In this article, we study the structure of finite inner Galois extensions and generalize several well-known properties of division algebras such as the Skolem-Noether theorem or the characterization to be a crossed product. We also describe, for any field K, the analoguous of the Brauer group for K: it is a certain subset of the Brauer group of the center of K, Br(Z(K)), which gives a one-to-one correspondance with the set of finite innner Galois and central extensions of K. (c) 2022 Elsevier Inc. Tous droits reserves.