| 保持二元布尔半环上矩阵的传递闭包的线性算子 |
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| 引用本文： | 邓伟娜,赵宪钟. 保持二元布尔半环上矩阵的传递闭包的线性算子[J]. 山东大学学报(理学版), 2022, 57(12): 64-70. DOI: 10.6040/j.issn.1671-9352.0.2022.044 |
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| 作者姓名： | 邓伟娜 赵宪钟 |
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| 作者单位： | 1.西北大学数学学院, 陕西 西安 710127;2.黄淮学院数学与统计学院, 河南 驻马店 463000 |
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| 基金项目： | 国家自然科学基金资助项目(11971383) |
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| 摘 要： | 研究保持二元布尔半环上矩阵的传递闭包的线性算子，给出保持传递闭包的可逆线性算子的刻画，并证明当矩阵的阶n≥2时，强保持传递闭包的线性算子一定是可逆的。
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| 关 键 词： | 二元布尔半环 矩阵 线性算子 传递闭包 |
Linear operators preserving transitive closures of matrices over the binary Boolean semiring |
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| DENG Wei-na,ZHAO Xian-zhong. Linear operators preserving transitive closures of matrices over the binary Boolean semiring[J]. Journal of Shandong University, 2022, 57(12): 64-70. DOI: 10.6040/j.issn.1671-9352.0.2022.044 |
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| Authors: | DENG Wei-na ZHAO Xian-zhong |
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| Affiliation: | 1. School of Mathematics, Northwest University, Xian 710127, Shaanxi, China;2. School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, Henan, China |
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| Abstract: | The linear operators which preserve transitive closures of matrices over the binary Boolean semiring are studied, the characterizations of invertible linear operators which preserve transitive closures of matrices are given, and it is shown that the strong preservers are invertible when the order of the matrices n≥2. |
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| Keywords: | binary Boolean semiring matrix linear operator transitive closure |
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