态射和的Drazin逆

The Drazin Inverse of a Sum of Morphisms

设C是加法范畴,态射φ,η:X→X是C上的态射。若φ,η具有Drazin逆且φη=0,则φ+η也具有Drazin逆。若φ具有Drazin逆φ~D且1x+φ~Dη可逆,作者讨论f=φ+η的Drazin逆(群逆)并且给出f^D(f~#)=(1x+φDη)^(-1)φ~D的充分必要条件。最后,把Huylebrouck的结果从群逆推广到了Drazin逆。

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 1x ＋ φ^Dη is invertible. We study the Drazin inverse （resp. group inverse） of f = φ ＋ η and give the necessary and sufficient condition for （resp. f^# （1x＋φ^Dη）^-1φ^D. Finally, we extend the Huylebrouck＇s result from the group inverse to the Drazin inverse.