Abstract
An element of a ring is called strongly nil clean provided that it can be written as the sum of an idempotent and a nilpotent element that commute. We characterize, in this article, the strongly nil cleanness of matrices over projective-free rings in terms of the factorizations of their characteristic polynomials.
ACKNOWLEDGMENTS
The author is grateful to the referee for his/her suggestions which provided the references [Citation4, Citation5] and led to the new version of the Section 4 more clearer. The research of the author is supported by the Natural Science Foundation of Zhejiang Province (Y6090404) and the Fund of Hangzhou Normal University.
Notes
Communicated by V. A. Artamonov.