具有有限内射维数的广义倾斜模(英文)

Generalized Tilting Modules With Finite Injective Dimension

设R和S分别为左、右Noether环,RωS为一个平衡的广义倾斜双模.本文给出了1.id_R(ω)≤1的一个等价刻画.并且在1.id_R(ω)和r.id_S(ω)均有限时讨论了Rω或ωS何时是内射的.此外,作为一个推论,得到一些Gorenstein环是QF-环的等价条件.

Let R be a left Noetherian ring,S be a right Noetherian ring and_Rω be a generalized tilting module with S = End(_Rω).We mainly consider the conditions such that l.id_R(ω) < 1 in this paper and obtain some characterizations for this inequality.Further,when l.id_R(ω) and r.id_S(ω) are finite,we provide the conditions such that_rω and ω_S are injective.As a direct application,we get some necessary and sufficient conditions for a Gorenstein ring to be a QF-ring.