The concept of FCGP-regular rings and FCGP-IF rings are given.The relations among regular rings, FCGP-regular rings, IF rings and FCGP-IF rings are proved.Finally, it elaborates semisimple rings.

• 其次，引入FCGP-正则环和FCGP-IF环的概念，证明了正则环、FCGP-正则环和IF环、FCGP-IF环之间的关系，并给出半单环的刻划。