Geodesic
On the set of all generalized Drazin invertible elements in a ring
Filomat, Tome 37 (2023) no. 20, p. 6719

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DOI

Berkani and Sarihr [Studia Math. (2001) 148: 251–257] showed that the set of all Drazin invertible elements in an algebra over a filed is a regularity in the sense of Kordula and M¨ uller [Studia Math. (1996) 119: 109–128]. In this paper, the above result is extended to the case of a ring. Counterexamples are provided to show that the set of all generalized Drazin invertible elements in a ring need not be a regularity in general. We determine when the set of all generalized Drazin invertible matrices in the 2 × 2 full matrix ring over a commutative local ring is a regularity. We also give a sufficient condition for the set of all generalized Drazin invertible elements in a ring to be a regularity
DOI : 10.2298/FIL2320719P
Classification : 16U90
Keywords: Regularity, Drazin inverse, Generalized Drazin inverse, Ring 
Fei Peng; Xiaoxiang Zhang. On the set of all generalized Drazin invertible elements in a ring. Filomat, Tome 37 (2023) no. 20, p. 6719 . doi: 10.2298/FIL2320719P
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     title = {On the set of all generalized {Drazin} invertible elements in a ring},
     journal = {Filomat},
     pages = {6719 },
     year = {2023},
     volume = {37},
     number = {20},
     doi = {10.2298/FIL2320719P},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2320719P/}
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