On Galois matrix rings of a ring

Abstract

Let R be a ring with 1, M_n(R) the ring of n × n-matrices over R for an integer n, and G an inner automorphism group of M_n(R) of order n² induced by {U_i ∈ M_n(R), i = 1, ... , n²}. Then the Galois matrix ring M_n(R) over R with inner Galois group G is characterized in terms of {U_i} and the trace of G.