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arXiv · 2510.00901

On the $(b, c)$-inverse of a sum with a radical element in a ring

Yukun Zhou·Nestor Thome
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Abstract

Let $R$ be a ring with identity and $J(R)$ be its Jacobson radical. Assume that $a\in R$ is $(b,c)$-invertible and $j_a,j_b,j_c\in J(R)$. This paper provides necessary and sufficient conditions for $a+j_a$ to be $(b+j_b,c+j_c)$-invertible. As an application, corresponding results on $(\widehat{B},\widehat{C})$-inverses of a dual matrix $\widehat{A}$ are derived.

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Yukun Zhou, Nestor Thome. 2025-10-01. On the $(b, c)$-inverse of a sum with a radical element in a ring. https://arxiv.org/abs/2510.00901

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