Let [Formula: see text] be a semiprime ring, not necessarily with unity, and [Formula: see text]. Let [Formula: see text] (respectively, [Formula: see text]) denote the set of inner (respectively, reflexive) inverses of [Formula: see text] in [Formula: see text]. It is proved that if [Formula: see text], then [Formula: see text] if and only if [Formula: see text] for all [Formula: see text]. As an immediate consequence, if [Formula: see text], then [Formula: see text] (see Theorem 7 in [A. Alahmadi, S. K. Jain and A. Leroy, Regular elements determined by generalized inverses, J. Algebra Appl. 18(7) (2019) 1950128] for rings with unity). We also give a generalization of Theorem 10 in [A. Alahmadi, S. K. Jain and A. Leroy, Regular elements determined by generalized inverses, J. Algebra Appl. 18(7) (2019) 1950128] by proving that if [Formula: see text] then [Formula: see text].