关于幂等元之差的可逆性

本文研究在一个有单位元的环中两个幂等元之差的可逆性问题,利用幂等元的性质,得到了两个幂等元之差可逆的几个充分必要条件,并给出了在矩阵环中的几个应用.     

倍幂等元与倍对合元的换位子的可逆性

本文研究在一个有单位元的环中两个倍幂等元的换位子与两个倍对合元的换位子的可逆性问题.利用倍幂等元和倍对合元的性质,得到了两个倍幂等元的换位子与两个倍对合元的换位子可逆的几个充要条件,揭示了倍幂等元和倍对合元与它们的换位子的内在联系.     

关于四个三幂等阵线性组合的可逆性和群逆（英文）

本文研究了四个三幂等阵线性组合的可逆性及群逆.利用矩阵分解的方法,获得了它们可逆及群逆的一些条件,并得到其逆和群逆的计算公式,这些结论完善了k幂等阵可逆性理论.     

关于四个三幂等阵线性组合的可逆性和群逆

本文研究了四个三幂等阵线性组合的可逆性及群逆.利用矩阵分解的方法,获得了它们可逆及群逆的一些条件,并得到其逆和群逆的计算公式,这些结论完善了k幂等阵可逆性理论.     

一类幂等元模J(R)可强提升的环

将Nicholson提出的幂等元强提升概念进行了推广,定义了L-环,弱L-环,使用通常环论方法研究了L-环中本原幂等元的Local性和L-环与potent环之间的关系,证明了一个环是L-环的充分必要条件是R/J(R)是Boole环,且幂等元模J(R)可强提升,同时对具有一对零同态的Morita Context环C=A VW B,关于L-性讨论了C与A,B之间的关系.     

幂等矩阵的组合的可逆性

本文研究了两个幂等矩阵P与Q的组合aP+bQ-cPQ-dQP-ePQP (其中a,b,c,d,e∈(C),a≠0,b≠0)的可逆性. 利用P-Q的可逆性及幂等矩阵的性质,得到了aP+bQ-cPQ-dQP-ePQP可逆的一些充要条件. 推广了J. J.Koliha 和 V.RakoA(c)eviA(c)[1]及Zuo Kezheng[2]的结论.     

正则幂环的同态与同构

随着模糊数学的发展,各种代数结构的提升为得越来越重要,李洪兴教授在「１,２」中首次提出并研究了幂群及ＨＸ环,本文在文「３～６」的基础上深入讨论了幂环的一些性质,并在正则幂环中建立了几个同态与同构定理。     

由环的幂零性所确定的根

结合环中的环的幂零性不是根性质。为此，本文将结合环中的幂零理想概念扩展为次拟幂零理想和拟幂零理想，定义次拟幂零根ＳＮ和拟幂零根ＱＮ，证明它们均为Ａｍｉｔｓｕｒ－Ｋｕｒｏｓｈ根，且二者相等，进一步，我们给出了ＱＮ－半单环的构造命题和ＱＮ－根的模刻划。     

交换局部环上强J-clean矩阵（英文）

环中元素称为强J-clean,如果它可写成幂等元与其Jacobson根中元素之和,并且它们可交换.本文研究了交换局部环上强J-clean 2×2矩阵,进而确定了素数p生成的素理想的局部化环Z_(p)和p-adic整数环Z_p上强J-clean 2×2矩阵.     

幂等元半环簇P

幂等元半环簇和幂等元分配半环簇依次记为I,ID.满足附加恒等式xyx x xyx=xyx的幂等元半环簇的子簇记为P.本文主要刻划了P中成员的一些性质,并对P∩ID中的部分成员进行了次直积分解.     

Invertibility of the Sum of Idempotents

We study necessary and sufficient conditions for the invertibility of the sum f+g when f and g are idempotents in a unital ring or bounded linear operators in Hilbert or Banach spaces. We describe the relation between the invertibility of f+g and f -g.     

Invertibility of the Sum of Idempotents

We study necessary and sufficient conditions for the invertibility of the sum f+g when f and g are idempotents in a unital ring or bounded linear operators in Hilbert or Banach spaces. We describe the relation between the invertibility of f+g and f m g.     

On the invertibility of Hilbert space idempotents

This note is to present some results on the group invertibility of linear combinations of idempotents when the difference of two idempotents is group invertible.     

Characterizations and representations of the group inverse involving idempotents

This paper is to present some results on the group invertibility of products and differences of idempotents. In addition, some formulae for the group inverse of sums, differences and products of idempotents are established by using some given idempotents.     

Characterizations and representations of the Drazin inverse involving idempotents

This paper is to present some results on the Drazin invertibility of products and differences of idempotents. In addition, some formulae for the Drazin inverse of sums, differences and products of idempotents are also established.     

ON THE INVERTIBILITY OF HILBERT SPACE IDEMPOTENTS

This note is to present some results on the group invertibility of linear combina- tions of idempotents when the difference of two idempotents is group invertible.     

Invertibility of the Difference of Idempotents

We study conditions equivalent to the invertibility of f -g when f and g are idempotents in a unital ring, and give applications to bounded linear operators in Banach and Hilbert spaces. In the setting of rings we are able to show that many conditions previously linked to finite dimensionality, rank equalities, norm topology of bounded linear operators or to properties of C *-algebras can be in fact proved by simple algebraic arguments.     

Hilbert空间上线性算子的Drazin可逆性

主要研究了Hilbert空间上两个Drazin可逆算子和的Drazin可逆性.同时,对上三角算子矩阵的Drazin可逆性也给出了详细的讨论.