On a functional identity involving inverses on matrix rings

Abstract

Let D be a division ring which is not a field with characteristic different from 2 and 3, and R = M_n(D) with n > 1. The purpose of this paper is to characterize additive maps f; g : R → R satisfying the functional identity f(X) + X²g(X ^-1) = 0 for all invertible X є R.