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Introduction. The outer Galois theory, started by Jacobson  , 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  and Jacobson  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  for simple algebras (finite over theirdoi:10.1090/s0002-9947-1952-0049875-3 fatcat:qsvmzyjax5c6jj7jhqaz5y7t6a