TSIU-KWEN LEE2021-07-212021-07-2120212194988https://www.scopus.com/inward/record.uri?eid=2-s2.0-85081963009&doi=10.1142%2fS0219498821500572&partnerID=40&md5=7d46eab198dc61558fc2bbd3f5dd2fechttps://scholars.lib.ntu.edu.tw/handle/123456789/572140Let 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]SDG10journal article10.1142/S02194988215005722-s2.0-85081963009