Group invertibility of the sum in rings and its applications

IF 0.8 4区数学 Q2 MATHEMATICS

Georgian Mathematical Journal Pub Date : 2024-03-25 DOI:10.1515/gmj-2024-2010

Huanyin Chen, Dayong Liu, Marjan Sheibani

引用次数: 0

Abstract

We present necessary and sufficient conditions under which the sum of two group invertible elements in a ring is group invertible. As applications, we establish the existence of group inverses of certain 2 × 2

{2\times 2}

block-operator matrices over a Banach space. These generalize the known results, e.g., Zhou, Chen and Zhu (Comm. Algebra 48 (2020), 676–690) and Benítez, Liu and Zhu (Linear Multilinear Algebra 59 (2011), 279–289).

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环中和的群可逆性及其应用

我们提出了环中两个群可逆元素之和是群可逆的必要条件和充分条件。作为应用，我们建立了巴拿赫空间上某些 2 × 2 {2\times 2} 块操作矩阵的群逆存在性。这些结果概括了已知结果，如 Zhou, Chen and Zhu (Comm.代数 48 (2020), 676-690) 和 Benítez、Liu 和 Zhu (Linear Multilinear Algebra 59 (2011), 279-289).

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Georgian Mathematical Journal 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Georgian Mathematical Journal was founded by the Georgian National Academy of Sciences and A. Razmadze Mathematical Institute, and is jointly produced with De Gruyter. The concern of this international journal is the publication of research articles of best scientific standard in pure and applied mathematics. Special emphasis is put on the presentation of results obtained by Georgian mathematicians.