Projections for generalized inverses

[EN] Let R be a unital ring with involution. In Section 2, for given two core invertible elements a, b. R, we investigate mainly the absorption law for the core inverse in virtue of the equality of the projections aa and .In Section 3, we study several relations concerning the projections a a and bb , where a . a{1, 2, 4} and b . b{1, 2, 3}. Some well- known results are extended to the *- reducing ring case. As an application, EP elements in a *- reducing ring are considered.This research was supported by the National Natural Science Foundation of China [grant number 11371089]. The first author is grateful to China Scholarship Councilor giving him a scholarship for his further study in Universitat Politecnica de Valencia Spain.Xu, S.; Chen, C.; Benítez López, J. (2018). Projections for generalized inverses. Linear and Multilinear Algebra. 66(8):1593-1605. https://doi.org/10.1080/03081087.2017.1364339S1593160566