Representability of Matrices over Commutative Rings as Sums of Two Potent Matrices.

We propose some general approach to studying the problem for the representability of every element in a field in the form , with and , where are fixed naturals, to imply the analogous representability of every square matrix over . As an application, we describe the fields and commutative rings with such that every square matrix over them is the sum of a -potent matrix and a -potent matrix for some small values of and . [ABSTRACT FROM AUTHOR]