Group invertibility of the sum in rings and its applications

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 kno...

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Bibliographic Details
Published inGeorgian mathematical journal
Main Authors Chen, Huanyin, Liu, Dayong, Sheibani, Marjan
Format Journal Article
LanguageEnglish
Published 26.03.2024
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Summary: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).
ISSN:1072-947X
1572-9176
DOI:10.1515/gmj-2024-2010