关于PP环和PF环

On PP Rings and PF Rings

证明了环Ｒ为左ＰＰ环的充要条件是Ｒ的任一非空子集的右零化子是纯理想．引入ＰＦＲ－模并给出了环Ｒ为ＰＦ环的一个充要条件是ＰＦＲ－模的子模仍为ＰＦＲ－模．

Prove that a ring R is left PP ring if and only if for each XR (X≠ ).the right annihilator of X in R is Pure ideal.In the second part, introduce PF R-modules And show that a ring R is PF ring if and only if every submodule PF R-module is also PF Rmodule.