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

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 [5]. Some open problems are also mentioned.