摘要
运用同调代数知识证明了环R上的每个左模都是Gorenstein投射(内射)的当且仅当R为QF环;证明了当R是n-Gorenstein环时,所有的右R-模都是Gorenstein平坦的当且仅当是R为左IF环;还证明了每个Gorenstein投射(内射、平坦)右R-模都是投射(内射、平坦)的当且仅当R的弱整体维数有限.
In this paper the following are proved by knowledge of homological algbra:All left modules over a ring R are Gorenstein projective(injective)if and only if R is a QF ring.When R is an n-Gorenstein ring,each right R-module is Gorenstein flat if and only if R is a left IF ring.Each Gorenstein projective(injective,flat)right R-module is projective(injective,flat)if and only if R has finite weak global dimension.
作者
李冠戬
LI Guan-jian(Faculty of General Education and Foreign Language,Anhui Institute of Information Technology,Wuhu 241000,China;Foreign Language School Attached to Anhui Normal University East Campus,Wuhu 241100,China)
出处
《南宁师范大学学报（自然科学版）》
2023年第3期19-23,共5页
Journal of Nanning Normal University：Natural Science Edition
基金
安徽省高等学校省级质量工程项目(2021kcszsfkc200)。
