强VW-Gorenstein复形  

Strongly VW -Gorenstein complexes

作　　者：贾宏慧 赵仁育 JIA Hong-hui;ZHAO Ren-yu(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2023年第3期33-38,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11861055,12061061)。

摘　　要：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.

关 键 词：VW-Gorenstein模 强VW-Gorenstein复形 W-复形 CE W-复形 

分 类 号：O153.3[理学—数学]