| On Strongly $J$-Semiclean Rings |
| Received:April 08, 2019 Revised:March 17, 2020 |
| Key Words:
upper triangular matrix local ring strongly $J$-semiclean ring
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| Fund Project:Supported by the Excellent Course Project for Postgraduates of Hunan University of Science and Technology (Grant No.J52112). |
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| Abstract: |
| 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 general setting. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2020.04.003 |
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