On strongly J-semiclean rings
Received:April 08, 2019  Revised:January 16, 2020
Key Word: Upper triangular matrix   Local ring   Strongly J-semiclean ring.  
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Author NameAffiliationE-mail
Lunqun Ouyang Department of Mathematics, Hunan Scienceand Technology University ouyanglqtxy@163.com 
Gong Zhaoqing Department of Mathematics, Hunan Scienceand Technology University  
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      We in this note introduce a new concept, so called strongly $J$-semiclean ring, that is a generalization of strongly $J$-clean rings. We first observe the basic properties of strongly $J$-semiclean rings, constructing typical examples. We next investigate conditions on a local ring $R$ that imply that the upper triangular matrix ring $T_n(R)$ is a strongly $J$-semiclean ring. Also, the criteria on strong $J$-semicleanness of $2\times 2$ matrices in terms of a quadratic equation are given. As a consequence, several known results relating to strongly $J$-clean rings are extended to a more generally setting.
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