QF环性质向扩环上的传递  

On a Hereditary Property of QF Rings

作　　者：杨存洁[1] 

机构地区：[1]首都师范大学数学系

出　　处：《Journal of Mathematical Research and Exposition》1994年第4期603-606,共4页数学研究与评论（英文版）

摘　　要：设环Ａ是环Ｂ的扩环（记作Ａ／Ｂ），Ｂ是ＱＦ环，在本文中我们将证明在以下四种情形下Ａ也是ＱＦ环：（１）＿ＢＡ是有限生成自由的且Ａ／Ｂ是投射扩张．（２）Ａ／Ｂ是Ｆｒｏｂｅｎｉｕｓ的．（３）Ａ／Ｂ是可离且平坦的．（４）Ａ／Ｂ是Ｈ－可离的．Let ring A be an extension of ring B with B a QF ring,In this paper, we show thatA is also a QF ring if one of the following condition is satisfied:(1)_BA is a finitely gen-erated free module and A/B is a projective extension. (2)A/B is a Frobenius extension.(3)A/B is a separable extension and _BA is a flat module. A/B is an H-separable extension.

关 键 词：QF环 投射扩张 可离扩张 F扩张 

分 类 号：O153.3[理学—数学]