@article {
author = {Danchev, P.},
title = {Strongly nil-clean corner rings},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {43},
number = {5},
pages = {1333-1339},
year = {2017},
publisher = {Springer and the Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {We 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 Ko\c{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 $n\times n$ matrix ring $\mathbb{M}_n(R)$ is nil-clean.},
keywords = {Nil-clean rings,strongly nil-clean rings,idempotents,nilpotents,Jacobson radical},
url = {http://bims.iranjournals.ir/article_1028.html},
eprint = {http://bims.iranjournals.ir/article_1028_dd5007f3d112d2a8f52ea8300cd6810b.pdf}
}