Let R be a semiprime ring, not necessarily with unity, and a, b is an element of R. Let I(a) (respectively, Ref(a)) denote the set of inner (respectively, reflexive) inverses of a in R. It is proved that if I(a) boolean AND I(b) not equal empty set, then I(a) subset of I(b) if and only if b = awb = bwa for all w is an element of I(a). As an immediate consequence, if empty set not equal I(a) = I(b), then a = b (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 empty set not equal Ref(a) subset of Ref (b) then a = b.
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