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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (12): 64-70.doi: 10.6040/j.issn.1671-9352.0.2022.044

• • 上一篇    

保持二元布尔半环上矩阵的传递闭包的线性算子

邓伟娜1,2,赵宪钟1*   

  1. 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
  • 发布日期:2022-12-05
  • 作者简介:邓伟娜(1983— ),女,博士研究生,研究方向为半环代数理论. E-mail:dwei2002@163.com*通信作者简介:赵宪钟(1961— ),男,博士,教授,博士生导师,研究方向为半环代数理论. E-mail:zhaoxz@nwu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11971383)

Linear operators preserving transitive closures of matrices over the binary Boolean semiring

DENG Wei-na1,2, ZHAO Xian-zhong1*   

  1. 1. School of Mathematics, Northwest University, Xian 710127, Shaanxi, China;
    2. School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, Henan, China
  • Published:2022-12-05

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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。

关键词: 二元布尔半环, 矩阵, 线性算子, 传递闭包

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.

Key words: binary Boolean semiring, matrix, linear operator, transitive closure

中图分类号: 

  • O151.21
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