Volume 34, Issue 3
J-Clean and Strongly J-Clean Rings

Commun. Math. Res., 34 (2018), pp. 241-252.

Published online: 2019-12

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• Abstract

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 $a=e+w$ (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.

• Keywords

J-clean ring, strongly J-clean ring, generalized matrix ring

16U99, 16S50

xymls999@126.com (Yueming Xiang)

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@Article{CMR-34-241, author = {Xiang , Yueming and Ouyang , Lunqun}, title = {J-Clean and Strongly J-Clean Rings}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {34}, number = {3}, pages = {241--252}, abstract = {

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 $a=e+w$ (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.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2018.03.06}, url = {http://global-sci.org/intro/article_detail/cmr/13490.html} }
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 -

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 $a=e+w$ (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.

Yueming Xiang & Lunqun Ouyang. (2019). J-Clean and Strongly J-Clean Rings. Communications in Mathematical Research . 34 (3). 241-252. doi:10.13447/j.1674-5647.2018.03.06
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