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arXiv · 2602.14421

The higher order group inverse in a ring

Liu Dayong·Chen Huanyin
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Abstract

This paper introduces and studies the higher-order group inverse in a ring. We extend known properties of the higher-order group inverse from complex matrices to elements of a ring and, in the process, derive new results. We further characterize when a ring element can be expressed as the sum of a higher-order group element and a nilpotent element.

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Liu Dayong, Chen Huanyin. 2026-02-16. The higher order group inverse in a ring. https://arxiv.org/abs/2602.14421

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