On the Drazin index of regular elements
On the Drazin index of regular elements
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DOI：
10.2478/s11533-009-0015-6
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发表时间：
2009-05
影响因子：
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通讯作者：
P. Patrício;António Veloso Costa-
中科院分区：
文献类型：
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作者：
P. Patrício;António Veloso Costa-
已知环元素a的群逆a#的存在性等价于a2a− + 1 − aa−的可逆性，与a的冯诺依曼逆a−的选择无关。在本文中，我们将a的Drazin指数与a2a− + 1 − aa−的Drazin指数联系起来。当考虑代数闭域上的矩阵时，我们给出了另一种刻画。最后，我们提出一些问题和评论。
It is known that the existence of the group inverse a# of a ring element a is equivalent to the invertibility of a2a− + 1 − aa−, independently of the choice of the von Neumann inverse a− of a. In this paper, we relate the Drazin index of a to the Drazin index of a2a− + 1 − aa−. We give an alternative characterization when considering matrices over an algebraically closed field. We close with some questions and remarks.