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Jacobson's lemma via Groebner-Shirshov bases | | Xiangui Zhao
; | | Date: |
21 Feb 2017 | | Abstract: | Let $R$ be a ring with identity $1$. Jacobson’s lemma states that for any
$a,bin R$, if $1-ab$ is invertible then so is $1-ba$. Jacobson’s lemma has
suitable analogues for several types of generalized inverses, e.g., Drazin
inverse, generalized Drazin inverse, and inner inverse. In this note we give a
constructive way via Groebner-Shirshov basis theory to obtain the inverse of
$1-ab$ in terms of $(1-ba)^{-1}$, assuming the latter exists. | | Source: | arXiv, 1702.6271 | | Services: | Forum | Review | PDF | Favorites | |
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