The spectral rank and Drazin inverse in J-semisimple and torsion-free rings

Abstract

In a recent paper [1], Brits, Schulz and the second-named author introduced and studied the spectral rank in the setting of J-semisimple and torsion-free rings. In the present paper, we investigate the relationship between this spectral rank and Drazin invertibility in J-semisimple and torsion-free rings and prove generalizations of results established in [2]. Some open problems are also mentioned.

[1] M. Askes, R. Brits, and F. Schulz. The Spectral Rank of an Element in a Ring.
J. Algebra Appl., page 2550010, 07 2023.

[2] R. Brits, L. Lindeboom, and H. Raubenheimer. Rank and the Drazin Inverse
in Banach Algebras.Stud. Math., 177:211–224, 2006.