| 相对于环的自同态的(b, c)-逆 |
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| 引用本文： | 焦珺,李文喜,赵良.相对于环的自同态的(b, c)-逆[J].数学研究及应用,2023,43(4):433-446. |
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| 作者姓名： | 焦珺 李文喜 赵良 |
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| 作者单位： | 安徽工业大学数理科学与工程学院应用数学系, 安徽 马鞍山 243032 |
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| 基金项目： | 国家自然科学基金(Grant No.12161049). |
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| 摘 要： | 研究了相对于环的自同态的$(b, c)$-逆的相对性质.在更一般地条件下, 定义了一类新的广义逆, 即$\alpha$-$(b, c)$-逆. 通过具体例子说明了$\alpha$-$(b, c)$-逆与$(b, c)$-逆是完全不同的两类广义逆, 并研究了$\alpha$-$(b, c)$-逆与$(b, c)$-逆等价的条件. 此外, 还研究了$\alpha$-$(b, c)$-逆的强clean分解. 这些研究结果统一和推广了$(b, c)$- 逆上的若干已知结果.
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| 关 键 词： | $\alpha$-$(b c)$-逆 Cline公式 Jacobson引理 强clean分解 |
| 收稿时间： | 2022/7/6 0:00:00 |
| 修稿时间： | 2022/11/25 0:00:00 |
Relative $(b, c)$-Inverses with Respect to a Ring Endomorphism |
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| Jun JIAO,Wenxi LI,Liang ZHAO.Relative $(b, c)$-Inverses with Respect to a Ring Endomorphism[J].Journal of Mathematical Research with Applications,2023,43(4):433-446. |
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| Authors: | Jun JIAO Wenxi LI Liang ZHAO |
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| Institution: | School of Mathematics and Physics, Anhui University of Technology, Anhui 243032, P. R. China |
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| Abstract: | We study the relative properties of $(b, c)$-inverses with respect to a ring endomorphism. A new class of generalized inverses named $\alpha$-$(b, c)$-inverse is introduced and studied in a more general setting. We show by giving an example that $(b, c)$-inverses behave quite differently from $\alpha$-$(b, c)$-inverses. The condition that an $\alpha$-$(b, c)$-invertible element is precisely a $(b, c)$-invertible element is investigated. We also study the strongly clean decompositions for $\alpha$-$(b, c)$-inverses. Some well-known results on ($b, c$)-inverses are extended and unified. |
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| Keywords: | $\alpha$-$(b c)$-inverse Cline''s formula Jacobson''s lemma strongly clean decomposition |
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