Special elements in a ring related to Drazin inverses

Lebtahi Ep-Kadi-Hahifi Leila, Patrício Pedro, Thome Coppo Néstor Javier

2012

Linear and Multilinear Algebra

In this article, the existence of the Drazin (group) inverse of an element a in a ring is analysed when amk¿kan, for some unit k and m, n in N. The same problem is studied for the case when a*=ka^mk^{-1} and for the {k, s+1}- potent elements. In addition, relationships with other special elements of the ring are also obtained.