On Strongly Nil Gf -Clean Rings and Related Generalized Inverses

In this paper, we give a further study of strongly nil [Formula: see text]-clean rings. Some new characterizations and extension properties of strongly nil [Formula: see text]-clean rings are provided. Furthermore, motivated by the notion of strong Drazin inverses, we introduce a new type of generalized inverse which is closely related to strongly nil [Formula: see text]-clean elements, and we present basic properties and structures of this type of inverse.