关于QF－1环的若干性质

Some Properties of QF-1 Ring

Ｖ．Ｐ．Ｃａｍｉｌｌｏ证明了如果Ｊ（Ｒ）是有限生成，则交换内射的ＱＦ－１环是ＰＦ环。但对于一般情况，这还是一个未解决的问题。本文取消Ｊ（Ｒ）是有限生成的条件，在其它条件下，比如Ｊ（Ｒ）是诣零且Ｊ／Ｊ２有限生成的条件，也证明了交换内射的ＱＦ－１环是ＰＦ环。同时，在挠理论下讨论了右ＱＦ－１环与ＱＦ－１分式环的关系。

It is proved by V.P.Camillo that if J(R) is finitely generated. a commutative injective QF-1 ring R is PF.However,ingeneral,it is an open question whether or not a commutative injective QF-1 ring is PF.In this paper.show that it is true if J(R) has the property 1(e.g.J(R) is nil)and J(R)/J(R)￣2 is finitely generated.Meanwhile also discusses the relationship between right QF-1 rings and QF-1 rings of quotients