Galois theory of simple rings

Tadasi Nakayama
1952 Transactions of the American Mathematical Society  
Introduction. The outer Galois theory, started by Jacobson [8] , has been developed rather thoroughly [2; 3; 6; 12; 16]. The general Galois theory, dealing with general groups of automorphisms (with some restrictions though), has been established by Cartan [5] and Jacobson [9] in case of sfields. The purpose of the present paper is to offer a similar theory for simple rings with minimum condition(J). The same has been given in fact in Hochschild [7] for simple algebras (finite over their
more » ... e over their centers). But the method breaks down in the case of general simple rings, infinite over their centers, and a new approach is necessary(2). The writer [14] has recently shown that if A is a simple ring and C is a weakly normal (cf. §1 below) simple subring of A,
doi:10.1090/s0002-9947-1952-0049875-3 fatcat:qsvmzyjax5c6jj7jhqaz5y7t6a