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《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (12): 11-18.doi: 10.6040/j.issn.1671-9352.0.2023.156

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基于对合环中的广义逆元素刻画SEP元

梁佳辉,王龙,魏俊潮*   

  1. 扬州大学数学科学学院, 江苏 扬州 225002
  • 发布日期:2024-12-12
  • 通讯作者: 魏俊潮(1968— ),男,教授,硕士生导师,博士,研究方向为环上广义逆. E-mail:jcweiyz@126.com
  • 基金资助:
    国家自然科学基金资助项目(11901510)

Characterizing SEP elements based on generalized inverse elements in rings with involution

LIANG Jiahui, WANG Long, WEI Junchao*   

  1. College of Mathematical Science, Yangzhou University, Yangzhou 225002, Jiangsu, China
  • Published:2024-12-12

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摘要： 首先通过对给定方程的可解性以及构造群逆元、MP(Moore-Penrose)逆元以及可逆元方程,研究*-环R中SEP元的一些等价刻画;而后利用方程在给定集合中的解以及构造广义逆方程、双变量方程的一般解给出SEP元的新刻画。

关键词: EP元, 偏序等距元, SEP元, 对合环

Abstract: In this paper, we firstly study some characterizations of SEP elements in rings with involution by the solvability of certain equation and construct the group inverses, MP inverses and invertible elements; Then we depict SEP elements by the solution of the equations, generalized inverse equations and the general solution of bivariate equations in a certain set.

Key words: EP element, partial isometry element, strongly EP element, involution ring

中图分类号: 

  • O153.3
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[1] 官梦鸽,周海楠,魏俊潮. EP元的一些等价刻画[J]. 《山东大学学报(理学版)》, 2023, 58(8): 13-17.
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