单J-内射环的刻划

Some Characterizations on Simple J-injective Rings

设R是环,证明了:1)R是右Noether,右单J-内射环,且Sr≤eRR或R是右Goldie,右单J-内射环,且Sr≤eRR,则R是右QF环;2)如果R是左完全环且当Rk或kR是单左或右理想时,r(k)是有限生成的,则R是右QF环.推广了文献[2]中Nicholson W K,Park J K,Yousif M F的相关结论并使著名的Faith猜想有了新的进展.

Let R be a ring,this paper proves（1）if R is a right noether, right simple J - injective ring with Sr≤eRR, or if R is a right Goldie, right simple J - injective ring with Sr ≤eRR, then R is QF ring. （2） if R is a left perfect right simple J - injective ring and is finitely generated whenever Rk or kR is simple for k E R, then R is right QF ring. Some known results of Nicholson, Park, Yousif are obtained as corollaries. And that Faith conjectures have latest development.