The $(j,m)$-core inverse in rings with involution

Year 2020, Volume: 49 Issue: 5, 1676 - 1685, 06.10.2020

Sanzhang Xu Jianlong Chen Dijana Mosić

https://doi.org/10.15672/hujms.701870

Abstract

Let $R$ be a unital ring with involution. The $(j,m)$-core inverse of a complex matrix was extended to an element in $R$. New necessary and sufficient conditions such that an element in $R$ to be $(j,m)$-core invertible are given. Moreover, several additive and product properties of two $(j,m)$-core invertible elements are investigated and a order related to the $(j,m)$-core inverse is introduced.

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Keywords

Moore-Penrose inverse, (j-m) core inverse, EP element

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