Abstract
Let R be a ring. Existence criteria for the (b, c)-inverse are given. We present explicit expressions for the (b, c)-inverse by using inner inverses. We answer the question when the (b, c)-inverse of \(a\in R\) is an inner inverse of a. As applications, we give a unified theory of some well-known results of the \(\{1,3\}\)-inverse, the \(\{1,4\}\)-inverse, the Moore–Penrose inverse, the group inverse and the core inverse.
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Xu, S., Benítez, J. Existence Criteria and Expressions of the (b, c)-Inverse in Rings and Their Applications. Mediterr. J. Math. 15, 14 (2018). https://doi.org/10.1007/s00009-017-1056-x
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DOI: https://doi.org/10.1007/s00009-017-1056-x