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arXiv · 2012.10571

Generalized Zhou inverses in rings

Huanyin Chen·Marjan Sheibani Abdolyousefi
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Abstract

We introduce and study a new class of generalized inverses in rings. An element $a$ in a ring $R$ has generalized Zhou inverse if there exists $b\in R$ such that $bab=b, b\in comm^2(a), a^n-ab\in \sqrt{J(R)}$ for some $n\in {\Bbb N}$. We prove that $a\in R$ has generalized Zhou inverse if and only if there exists $p=p^2\in comm^2(a)$ such that $a^n-p\in \sqrt{J(R)}$ for some $n\in {\Bbb N}$. Cline's formula and Jacobson's Lemma for generalized Zhou inverses are established. In particular, the Zhou inverse in a ring is characterized.

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Huanyin Chen, Marjan Sheibani Abdolyousefi. 2020-12-19. Generalized Zhou inverses in rings. https://arxiv.org/abs/2012.10571

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