强VW-Gorenstein复形

Strongly VW -Gorenstein complexes

设V,W是两个R-模类。引入了强VW-Gorenstein复形的概念,证明了如果V,W关于扩张和有限直和封闭,并且V⊥V,W⊥W,V⊥W,V,WG(VW),那么复形M是强VW-Gorenstein的当且仅当M是正合复形,并且对任意的n∈Z,Z_(n)(M)是VW-Gorenstein模。此外,我们得到了一些有意义的推论,这些结果统一和推广了一些已知的结论。

Let V, W be two classes of R-modules. A notion of strongly V W-Gorenstein complexes is introduced. It is shown that if V, W are closed under extensions and finite direct sums, V ⊥V, W ⊥W, V ⊥W and V,W ?G(V W), a complex M is strongly V W-Gorenstein if and only if M is exact and Zn(M) is V W-Gorenstein for all n∈Z. In addition, some interesting corollaries are obtained, which unify and genelize some known results.