m-weak group inverses in a ring with involution

2020/07/31 by Yukun Zhou, Jianlong Chen, Zhou, Yukun +3 · 3 citations
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2007.15819

openalex publication_date 2020/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a unitary ring with involution, we prove that each element has at most one weak group inverse if and only if each idempotent element has a unique weak group inverse. Furthermore, we define the m-weak group inverse and show some properties of m-weak group inverse.

Citations

• A generalized inverse for matrices
• Core inverse of matrices
• Core–EP inverse
• The class ofm-EPandm-normal matrices
• Pseudo-Inverses in Associative Rings and Semigroups
• Characterizations of k-commutative equalities for some outer generalized inverses
• Pseudo core inverses in rings with involution

Cited by

• Additive properties and absorption laws for generalized inverses
• Generalized right group inverse in Banach *-algebras
• The m-generalized right group inverses in Banach algebras

Related

• m-weak group inverse in a ring with proper involution
• The inverse along an element in rings
• m-weak group MP inverse
• Further properties and representations of the W-weighted m-weak group inverse
• Algebraic properties of the group inverse