Yukun Zhou

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math.RA2025

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

Yukun Zhou, Nestor Thome

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 sufficie…

math.RA2025

Additive properties and absorption laws for generalized inverses

Yukun Zhou, Jianlong Chen, Nestor Thome

Let $a, f$ be elements in a ring with pseudo core inverses $a^{D ◯}$ , $f^{D ◯}$ , and let $b = f - a$ . We prove that the absorp…

math.RA2020

m-weak group inverses in a ring with involution

Yukun Zhou, Jianlong Chen, Mengmeng Zhou

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…

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

Additive properties and absorption laws for generalized inverses

m-weak group inverses in a ring with involution

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