A characterization of commutators of idempotents Original Research Article

Necessary and sufficient conditions are obtained for an element in a ring to be a commutator of idempotents. In the special case of finite-dimensional operators, it is shown that an operator T is a commutator of a pair of idempotents if and only if T is similar to −T and the Riesz part T1 of T corresponding to image has the property that image has a square root.