Turkish Journal of Mathematics
Abstract
Let $R$ be a ring and $a,b,c\in R$. We give a novel characterization of group inverses (resp. EP elements) by the properties of right (resp. left ) $c$-regular inverses of $a$ and discuss the relation among the strongly left $(b,c)$-invertibility of $a$, the right $ca$-regularity of $b$, and the $(b,c)$-invertibility of $a$. Finally, we investigate the sufficient and necessary condition for a ring to be a strongly left min-Abel ring by means of the $(b,c)$-inverse of $a$.
DOI
10.3906/mat-1804-32
Keywords
Right $c$-regular element, $(b, c)$-inverse, group inverse, $EP$ element, left min-Abel ring
First Page
3078
Last Page
3089
Recommended Citation
ZHAO, R, YAO, H, WANG, L, & WEI, J (2018). Some characterizations of right $c$-regularity and $(b,c)$-inverse. Turkish Journal of Mathematics 42 (6): 3078-3089. https://doi.org/10.3906/mat-1804-32
