Some Research On Group Inverse In Category

Some properties of the group inverse of morphisms are studied in this paper: First,we study the group inverse of a morphisms with (epic,monic) factorization in an additive category .And we give a necessary and sufficient condition of the existence and expression ofφ~# by constructing bi-products. Second, we give the necessary and sufficient condition forφto have the W-Drazin inverse, by using the Von Neumann regular inverse for theφ~k, extending the result on Drazin inverse in [28]. Finally, we discussed the M-group inverses of square matrices over complex field of special category . Some necessary and sufficient conditions for existence and some expressions of the M-group inverses are given ,by the minus inverse and the universal factorization respectively.