@article{95d838f2999c46e387dcb7867479a33e,
title = "JACOBSON{\textquoteright}S LEMMA FOR THE GENERALIZED n-STRONG DRAZIN INVERSES IN RINGS AND IN OPERATOR ALGEBRAS",
abstract = "In this paper, we extend Jacobson{\textquoteright}s lemma for Drazin inverses to the generalized n-strong Drazin inverses in a ring, and prove that 1−ac is generalized n-strong Drazin invertible if and only if 1−ba is generalized n-strong Drazin invertible, provided that a(ba)2 = abaca = acaba = (ac)2a. In addition, Jacobson{\textquoteright}s lemma for the left and right Fredholm op-erators, and furthermore, for consistent in invertibility spectral property and consistent in Fredholm and index spectral property are investigated.",
keywords = "Fredholm operator, Jacobson{\textquoteright}s lemma, consistent in invertibility, generalized n-strong Drazin inverse",
author = "Yanxun Ren and Lining Jiang",
note = "Publisher Copyright: {\textcopyright} 2022, University of Zagreb, Faculty of Mining, Geology and Petroleum Engineering. All rights reserved.",
year = "2022",
month = jun,
day = "28",
doi = "10.3336/gm.57.1.01",
language = "English",
volume = "57",
pages = "1--15",
journal = "Glasnik Matematicki",
issn = "0017-095X",
publisher = "Croatian Mathematical Society",
number = "1",
}