Jacobson’s lemma for the generalized Drazin inverse
Jacobson’s lemma for the generalized Drazin inverse
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DOI：
10.1016/j.laa.2011.07.044
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发表时间：
2012-02
影响因子：
1.1
通讯作者：
Guifen Zhuang;Guifen Zhuang;Jianlong Chen;Jian Cui
中科院分区：
文献类型：
--
作者：
Guifen Zhuang;Guifen Zhuang;Jianlong Chen;Jian Cui
研究了环中允许广义Drazin逆的元素的性质。证明了元素1-ab是广义Drazin可逆的当且仅当so是1-ba，并给出了1-ba的广义Drazin逆与1-ab的谱幂等元的关系式.此外，最近的结果有关的Drazin指数可以恢复从我们的定理。
0truemm0truemm We study 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 our theorems.