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arXiv · 2406.15745

m-weak group inverse in a ring with proper involution

Huanyin Chen
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Abstract

The m-weak group inverse was recently studied in the literature. The purpose of this paper is to investigate new properties of this generalized inverse for ring elements. We introduce the m-weak group decomposition for a ring element and prove that it coincides with its m-weak group invertibility. We present the equivalent characterization of the m-weak group inverse by using a polar-like property. The relations between m-weak group inverse and core-EP inverse are also established. These give some new properties of the weak group inverse for complex matrices and ring elements.

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Huanyin Chen. 2024-06-22. m-weak group inverse in a ring with proper involution. https://arxiv.org/abs/2406.15745

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