| 强$J$-Semiclean环 |
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| 引用本文： | 欧阳伦群,龚朝庆. 强$J$-Semiclean环[J]. 数学研究及应用, 2020, 40(4): 351-366 |
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| 作者姓名： | 欧阳伦群 龚朝庆 |
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| 作者单位： | 湖南科技大学数学与计算科学学院, 湖南 湘潭 411201 |
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| 基金项目： | 湖南科技大学研究生精品课程建设项目(Grant No.J52112). |
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| 摘 要： | 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 × 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.
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| 关 键 词： | 上三角形 局部环 强$J$-semiclean环 |
| 收稿时间： | 2019-04-08 |
| 修稿时间： | 2020-03-17 |
On Strongly $J$-Semiclean Rings |
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| Lunqun OUYANG,Zhaoqing GONG. On Strongly $J$-Semiclean Rings[J]. Journal of Mathematical Research with Applications, 2020, 40(4): 351-366 |
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| Authors: | Lunqun OUYANG Zhaoqing GONG |
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| Affiliation: | Department of Mathematics, Hunan University of Science and Technology, Hunan 411201, P. R. China |
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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 $2times 2$ 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. |
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| Keywords: | upper triangular matrix local ring strongly $J$-semiclean ring |
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