Rings over which matrices are products of q-potents.

Let R be a commutative ring, m>1 an integer and q>1 an odd number. The following questions are addressed: (1) when is every element in M n (R) and, respectively, in T n (R) a product of q-potents? (2) when is every element in M n (R) and, respectively, in T n (R) a product of mq-potents? and (3) when is every element in M n (R) and, respectively, in T n (R) a product of an idempotent and a q-potent? [ABSTRACT FROM AUTHOR]