We prove some results for the group inverse of elements in a unital ring. Thus, some results from (C. Deng, Electronic J. Linear Algebra 31 (2016)) are extended to more general settings.
We investigate perturbations of the Moore–Penrose inverse and forward order law for the Moore–Penrose inverse in rings with involution, and thus we extend some results of Castro–Gonzalez and Hartwig to more general settings.
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