FPF环和AUT-PIC性质

设R是—FPF环（不要求交换），本文研究了R的一些性质并给出了R上的有限生成投射左R-模的两种直和分解．在本文的第三部分，我们证明了以下结果：（a）FPF环具有Aut－Pic性质．（b）R有Aut-Pic性质当且当R／I有Aut－Pic性质，I是R的根式理想．（c）作为Aut－Pic性质的一个应用，定理3.3推广了9]中的一个结果．

FPF Rings and the Aut-Pic Property

We consider properties of FPF rings (need not to be commutative) and give two types of direct sum decompositions of a finitely generated projective moduls. We prove the following results: (a) FPP rings have the Aut-Pic property. (b) A ring R has the Aut-Pic property if and only if R/I has the Aut-Pic property, where I is a radical ideal of R. (c) Finally, as an application of the Aut-Pie property, Theorem 3.3 generalizes a result in 9].