Jacobson’s lemma for the generalized Drazin inverse
Copyright policy )Jacobson’s lemma for the generalized Drazin inverse
The authors investigate some properties of elements in a ring which admit the generalized Drazin inverse. It is shown that the element \(1-ab\) is generalized Drazin invertible if and only if so is \(1-ba\) and a formula for the generalized Drazin inverse of \(1-ba\) in terms of the generalized Drazin inverse and the spectral idempotent of \(1-ab\) is provided. Further, recent results relating to the Drazin index can be recovered from the theorems in this paper.
- Jiangnan University China (People's Republic of)
- Southeast University China (People's Republic of)
- Xiangnan University China (People's Republic of)
Numerical Analysis, Algebra and Number Theory, generalized Drazin inverse, Spectral idempotent, Drazin index, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), regular element, Generalized Drazin inverse, Discrete Mathematics and Combinatorics, Theory of matrix inversion and generalized inverses, Drazin inverse, Geometry and Topology, Regular element, spectral idempotent
Numerical Analysis, Algebra and Number Theory, generalized Drazin inverse, Spectral idempotent, Drazin index, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), regular element, Generalized Drazin inverse, Discrete Mathematics and Combinatorics, Theory of matrix inversion and generalized inverses, Drazin inverse, Geometry and Topology, Regular element, spectral idempotent
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