Exchange的GCN环

Exchange GCN rings

研究了GCN环的相关性质及应用,并证明了如下结论:1)设R为一个exchange的GCN环,如果R的每个素理想是左本原的,则R为强π-正则环;2)一个环R为强正则环当且仅当R为半素的exchange的GCN环且每个素理想是左本原的;3)完全左幂等的exchange的GCN环是强正则环;4)设R为一个exchange的GCN环,则群环R[G]是von Neumann正则环当且仅当R[G]是完全左幂等环.

This paper is a further study of GCN ring. The main results are as follows： 1） Let R be an exchange GCN ring, if every prime ideal of R is left primitive, then R is a strongly π - regular ring; 2） A ring R is a strongly regular ring if and only if R is a semiprime exchange GCN ring and every prime ideal of R is left primitive; 3） Full left idempotent exchange GCN ring is a strongly regular ring; 4） Let R be an exchange GCN ring, group ring R[G] is avon Neumann regular ring if and only if R[G] is a full left idempotent ring.