Inclusion properties of generalized inverses in semiprime rings
Journal
Journal of Algebra and its Applications
Journal Volume
20
Journal Issue
4
Date Issued
2021
Author(s)
Abstract
Let R be a semiprime ring, not necessarily with unity, with extended centroid C. For a R, let T(a) (respectively I(a), Ref(a)) denote the set of all outer (respectively inner, reflexive) inverses of a in R. In the paper, we study the inclusion properties of T(a), I(a) and Ref(a). Among other results, we prove that for a,b R with a von Neumann regular, Ref(a) T(b) (respectively Ref(a) I(b)) if and only if a = E[a]b (respectively I(a) I(b)). Here, E[a] is the smallest idempotent in C such that E[a]a = a. This gives a common generalization of several known results. ? 2021 World Scientific Publishing Company.
SDGs
Type
journal article