态射的分解与Moore-Penrose逆

Factorization of Morphisms and Moore-Penrose Inverse

通过态射的分解讨论预加法范畴中态射的Moore-Penrose逆。给出了态射的Moore-Penrose逆存在的几个充要条件以及表达式。特别,得到了态射f有Moore-Penrose逆的充要条件是f有泛分解f=pgq使得g+存在并且(pg)*pg+i-g+g和gq(gq)*+i-gg+均可逆。

By use of factorization of morphisms, the Moore-Penrose inverses of morphisms in the preadditive category are discussed. Some necessary and sufficient conditions for existence of the Moore-Penrose inverse of morphisms and some characterizations of the Moore-Penrose inverse are given. In particular, the Moore-Penrose inverse of a morphism f exists if and only if there exist morphisms p,g and q such that f=pgq,g^＋ exists, and （pg）^＊ pg＋i-g^＋g and gq（gq）^＊ ＋i-gg^＋ are both invertible.