Power commuting traces of bilinear maps on invertible elements

Abstract

Let [Formula: see text] be a unital simple ring. Under a mild technical restriction on [Formula: see text], we characterize bilinear mappings [Formula: see text] satisfying [Formula: see text], and [Formula: see text] for all unit [Formula: see text] and [Formula: see text], where [Formula: see text]. As an application we describe bijective linear maps [Formula: see text] satisfying [Formula: see text] for all invertible [Formula: see text]. Precisely, we will show that [Formula: see text] is an isomorphism.