It is known that the existence of the group inverse a # of a ring element a is equivalent to the invertibility of a 2 a − + 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 a 2 a − + 1 − aa −. We give an alternative characterization when considering matrices over an algebraically closed field. We close with some questions and remarks.
@article{bwmeta1.element.doi-10_2478_s11533-009-0015-6,
author = {Pedro Patr\'\i cio and Ant\'onio Costa},
title = {On the Drazin index of regular elements},
journal = {Open Mathematics},
volume = {7},
year = {2009},
pages = {200-205},
zbl = {1188.15005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0015-6}
}
Pedro Patrício; António Costa. On the Drazin index of regular elements. Open Mathematics, Tome 7 (2009) pp. 200-205. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0015-6/
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