Centralizer's applications to the (b,c)-inverses in rings

作者:Xu, Sanzhang*; Chen, Jianlong; Benitez, Julio; Wang, Dingguo
来源:Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales Serie A-Matematicas, 2019, 113(3): 1739-1746.
DOI:10.1007/s13398-018-0574-0

摘要

We give several conditions in order that the absorption law for one sided (b,c)-inverses in rings holds. Also, by using centralizers, we obtain the absorption law for the (b,c)-inverse and the reverse order law of the (b,c)-inverse in rings. As applications, we obtain the related results for the inverse along an element, Moore-Penrose inverse, Drazin inverse, group inverse and core inverse.