Affiliation:
1. School of Mathematics, Southeast University, Nanjing, China
Abstract
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?ller [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.
Publisher
National Library of Serbia
Reference18 articles.
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4. J. Cui, Quasinilpotents in rings and their applications, Turkish J. Math. 42 (2018), 2847-2855.
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