相关正则环和IF环(英文)

Relative Regular Ring and IF Ring

本文定义了在左 M-正则环和左 M-IF环 ,并利用 M-平坦模和 M-内射模对两类环进行了刻画 (定理 1 .5,定理 1 .6和定理 2 .2 ) ,同时还利用左 M-正则环、左 M-IF环、M-平坦模和 M-投射模 ,刻画出了正则环和左 M-IF环 (定理 1 .7,推论 2 .3和推论 2 .5)

In this paper,we give some characterizations of left M regular rings and left M IF rings by M flat module and M projective modules (Theorems1.5,1.6 and 2.2).We describe the relations on left regular rings,left M regular rings and left M IF ring left IF rings.By the left M regular ring and left M IF ring,M flat module and M projective module,we also describe left regular ring and left IF ring (Theorem 1.7,Corollaries 1.8,2.3and 2.5 of Theorem 1.7).