Suitable elements, *-clean elements and Sylvester equations in rings with involution

被引：1

作者：

Zhu, Huihui ^{[1
]}

Wu, Liyun ^{[1
]}

Wang, Qing-Wen ^{[2
]}

机构：

[1] Hefei Univ Technol, Sch Math, Hefei, Peoples R China

[2] Shanghai Univ, Dept Math, Shanghai, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2022年 / 50卷 / 04期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

*-Clean elements; regularities; suitable elements; Sylvester equations; INVERSE;

D O I：

10.1080/00927872.2021.1985129

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a *-ring. In this article, we introduce good *-clean elements and left *-suitable elements in R, respectively. An element a is an element of R is good *-clean if it can be written as the sum of a projection and a unitary element. An element a is an element of R is left *-suitable if there exists a projection p is an element of Ra such that 1-p is an element of R(1-a). Several properties of them are given and their characterizations are derived by the solvability of the Sylvester equation XA-BX=C in a ring. Finally, we use generalized inverses to give the existence criterion of left *-suitable elements.

引用

页码：1535 / 1543

页数：9