- Hacettepe Journal of Mathematics and Statistics
- Vol: 49 Issue: 5
- The $(j,m)$-core inverse in rings with involution
The $(j,m)$-core inverse in rings with involution
Authors : Sanzhang Xu, Jianlong Chen, Dijana Mosić
Pages : 1676-1685
Doi:10.15672/hujms.701870
View : 9 | Download : 3
Publication Date : 2020-10-06
Article Type : Research
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. ***********************************************************************************************************************************Keywords : Moore-Penrose inverse, (j-m) core inverse, EP element