Springer and the Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43520171031Strongly nil-clean corner rings133313391028ENP.DanchevDepartment of Mathematics, University of Plovdiv, Plovdiv 4000, Bulgaria.Journal Article20160319We show that if $R$ is a ring with an arbitrary idempotent $e$ such that $eRe$ and $(1-e)R(1-e)$ are both strongly nil-clean rings, then $R/J(R)$ is nil-clean. In particular, under certain additional circumstances, $R$ is also nil-clean. These results somewhat improves on achievements due to Diesl in J. Algebra (2013) and to Koc{s}an-Wang-Zhou in J. Pure Appl. Algebra (2016). In addition, we also give a new transparent proof of the main result of Breaz-Calugareanu-Danchev-Micu in Linear Algebra Appl. (2013) which says that if $R$ is a commutative nil-clean ring, then the full $ntimes n$ matrix ring $mathbb{M}_n(R)$ is nil-clean.http://bims.iranjournals.ir/article_1028_dd5007f3d112d2a8f52ea8300cd6810b.pdf