Rings over Which Matrices Are Sums of Idempotent and q-Potent Matrices

Abstract

We study the rings over which each square matrix is the sum of an idempotent matrix and a q-potent matrix. We also show that if F is a finite field not isomorphic to F3 and q > 1 is odd then each square matrix over F is the sum of an idempotent matrix and a q-potent matrix if and only if q-1 is divisible by |F| - 1.