关键词: Drazin逆, 群逆, 态射

Abstract:

Let C be an additive category. Suppose that φ and η: X→ X are two morphisms of C. If φ and η have the Drazin inverses such that  φη=0, then φ+η has the Drazin inverse. If φ has the Drazin inverse  φ^D such that 1_X+φ^Dη  is  invertible. We study the Drazin inverse (resp. group inverse) of f =φ+η and give the necessary and sufficient condition for f^D(resp. f ^#}=(1_X+φ^Dη)^-1φ^D. Finally, we  extend the Huylebrouck's result from the group inverse to the Drazin inverse.

Key words: Drazin inverse, Group inverse, Morphism