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Let  R  be a commutative ring,  m &gt;1 an integer and  q &gt;1 an odd number. The following questions are addressed: (1) when is every element inand, respectively, ina product of  q -potents? (2) when is every element inand, respectively, ina product of  mq -potents? and (3) when is every element inand, respectively, ina product of an idempotent and a  q -potent?

Rings over which matrices are products of q -potents