Abstract
We study the generalization of Jacobson’s lemma for the group inverse, Drazin inverse, generalized Drazin inverse and pseudo Drazin inverse of \(1-bd\) (or \(1-ac\)) in a ring when \(1-ac\) (or \(1-bd\)) has a corresponding inverse, \(acd=dbd\) and \(bdb=bac\) (or \(dba=aca\)). Thus, we recover some recent results.
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Dijana Mosić: The author is supported by the Ministry of Education and Science, Republic of Serbia, Grant No. 174007.
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Mosić, D. Extensions of Jacobson’s lemma for Drazin inverses. Aequat. Math. 91, 419–428 (2017). https://doi.org/10.1007/s00010-017-0476-9
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DOI: https://doi.org/10.1007/s00010-017-0476-9