On Yaqub nil-clean ring
Abstract
A ring R is Yaqub nil-clean if for any a∈ R, a-a3 or a+a3 is nilpotent for all a∈ R. We prove that a ring R is Yaqub nil-clean if and only if for any a∈ R, there exists some e3=e∈ R, such that a-e or a+3e is nilpotent and ae=ea.
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