Argaç N.Ero?lu M.P.Lee T.-K.Lin J.-H.2023-01-122023-01-122020030810870308-1087https://doi.org/10.1080/03081087.2019.1575331https://hdl.handle.net/11454/79634Motivated by [1, 2], the goal of the paper is to study certain identities with inverses on matrix rings. Given D a division ring, we characterize additive maps f, g: D ? D satisfying the identity f(x)x?1 + xg(x?1) = 0 for all invertible x ? D. Let R be a matrix ring over a division ring of characteristic not 2. We also characterize additive maps f, g: R ? R satisfying the identity f(x)x?1 + xg(x?1) = 0 for all invertible x ? R. Precisely, there exist an element q ? R and a derivation d of R such that f(x) = xq + d(x) and g(x) = ?qx + d(x) for all x ? R. This affirmatively answers the question below Theorem 4 in [1] due to L. Catalano. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.en10.1080/03081087.2019.1575331info:eu-repo/semantics/closedAccess16K40derivationDivision ringfunctional identityinversematrix ringPrimary 16R60Article6836356512-s2.0-85061439185Q2