Special elements in a ring related to Drazin inverses

摘要

In this article, the existence of the Drazin (group) inverse of an element a in a ring is analysed when a~mk = ka~n, for some unit k and m, 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.