TY - JOUR
T1 - J-Clean and Strongly J-Clean Rings
AU - Xiang , Yueming
AU - Ouyang , Lunqun
JO - Communications in Mathematical Research 
VL - 3
SP - 241
EP - 252
PY - 2019
DA - 2019/12
SN - 34
DO - http://doi.org/10.13447/j.1674-5647.2018.03.06
UR - https://global-sci.org/intro/article_detail/cmr/13490.html
KW - J-clean ring, strongly J-clean ring, generalized matrix ring
AB - <p style="text-align: justify;">Let $R$ be a ring and $J(R)$ the Jacobson radical. An element $a$ of $R$ is
called (strongly) $J$-clean if there is an idempotent $e\in R$ and $w\in J(R)$ such that&nbsp;$a=e+w$ (and $ew=we$). The ring $R$ is called a (strongly) $J$-clean ring provided
that every one of its elements is (strongly) $J$-clean. We discuss, in the present paper,
some properties of $J$-clean rings and strongly $J$-clean rings. Moreover, we investigate $J$-cleanness and strongly $J$-cleanness of generalized matrix rings. Some known results
are also extended.</p>