2019/10/21 by Long Wang, Dijana Mosić · 1 citation
Mathematics · Computer Science · #Advanced Topics in Algebra #Matrix Theory and Algorithms #Rings, Modules, and Algebras
paper · doi:10.1080/03081087.2019.1679073
Let R be a ring and a,b,c∈R. In this paper, it is shown that if a is left (b,c)-invertible and cab is regular, then a has at least one regular left (b,c)-inverse. And the expression of the (b,c)-inverse of a is given in terms of the inner inverse of cab. Moreover, the strongly left (or right) (b,c)-inverse is introduced in terms of the regularity of cab. It is shown when (ab)∗=ab, a is left (b,b)-invertible implies that a is strongly left (b,b)-invertible, and left (b,b)-invertibility coincides with right (b,b)-invertibility. As applications, we consider when the one-sided core inverse is core invertible. It is shown that left core invertibility coincides with right core invertibility in every strongly π-regular ring.