Frobenius扩张下的W^(⊥)-Gorenstein内射性  

W⊥-Gorenstein injectivity under Frobenius extensions

作　　者：宋维[1] SONG Wei(Mathematics Teaching and Research Section, Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou 310053, China)

机构地区：[1]浙江机电职业技术学院数学教研室,浙江杭州310053

出　　处：《兰州理工大学学报》2022年第1期161-167,共7页Journal of Lanzhou University of Technology

基　　金：浙江省自然科学基金(LY16A010003)。

摘　　要：对于一个广义的倾斜模W_(R),定义了W^(⊥)_(R)-Gorenstein内射模和W^(⊥)_(R)-Gorenstein内射维数,证明了在环Frobenius扩张下,模的W^(⊥)-Gorenstein内射模性是保持的,即对于M_(R)、M_(R)是一个W^(⊥)_(R)-Gorenstein内射模当且仅当M_(R)S_(S)是一个(W_(R)S_(S))^(⊥)_(S)-Gorenstein内射模,并讨论了模的W^(⊥)_(R)-Gorenstein内射维数在Frobenius扩张下的保持性.此外,作为应用,得到了一些与同调维数相关的有意义的推论.The notions of W^(⊥)_(R)-Gorenstein injective module and W^(⊥)_(R)-Gorenstein injective dimension respect to a generalized tilting moduleW_(R),and it is prove that the W^(⊥)-Gorenstein injectivity is preserved under Frobenius extensions,that is,for a Frobenius extension S/R and an R-ModuleM_(R),M_(R) is W^(⊥)_(R)-Gorenstein injective if and only if M_(R)S_(S) is(W_(R)S_(S))^(⊥)_(S)-Gorenstein injective.Some properties of W^(⊥)_(R)-Gorenstein injective dimension are obtained.Furtheremore,as an applications,some valuable corollaries about some classical homological dimension as applications.

关 键 词：广义倾斜模 Frobenius扩张 W^(⊥)-Gorenstein内射模 

分 类 号：O154.2[理学—数学]