On Galois theory of division rings

Abstract

Recently N. Nobusawa has succeeded to generalize Krull’s Galois theory for fields of infinite degree o division rings. But in his paper he discussed separately the compac Galois group and the discrete Galois group. In our investigation, considering the locally compact case, we can discuss the above wo cases a he same ime, moreover the discussion will present a generalization of Nobusawa’s theory. In his note, we shall state our results withou proofs.