Lee T.-K.2022-11-152022-11-15202202194988https://www.scopus.com/inward/record.uri?eid=2-s2.0-85128573316&doi=10.1142%2fS0219498823501359&partnerID=40&md5=370fe6ff9b28976a82dbe2beeaddd65ahttps://scholars.lib.ntu.edu.tw/handle/123456789/625097An element b in a unital ring R is said to have an inverse complement c if b + c is a unit of R and bR cR = 0. Unit-regular elements are studied from the viewpoint of the existence of inverse complements. As a source of unit-regular elements, we prove that if MR is a completely reducible submodule of RR, then every element of M is unit-regular if and only if any nonzero submodule of MR is not square zero. This generalizes some results due to Stopar in 2020. Finally, extending the case of real or complex matrices to the context of rings, we characterize the outer and reflexive inverses of a given unit-regular element depending only on its inverse complement. © 2023 World Scientific Publishing Company.(left) right disjoint; completely reducible module; inner (outer, reflexive) inverse; inverse complement; minus partial order; Unit-regularjournal article10.1142/S02194988235013592-s2.0-85128573316