Abstract
Let R be a unit-regular ring, and let a, b, c ? R satisfy aba = aca. If ac or ba is Drazin invertible, we prove that their Drazin inverses are similar. Furthermore, if ac and ba are group invertible, then ac is similar to ba. For any n?n complex matrices A, B,C with ABA = ACA, we prove that AC and BA are similar if and only if their k-powers have the same rank. These generalize the known Flanders? theorem proved by Hartwig.
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