QF环性质向扩环上的传递

On a Hereditary Property of QF Rings

中文关键词:  QF环  投射扩张  Frobenius扩张  可离扩张  平坦  H－可离扩张．

中文摘要:

      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．

英文摘要:

      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.