Homology of artinian and Matlis reflexive modules, I

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• 作者：Bethany Kubik^a ; ^{bethany.kubik@ndsu.edu} ; ; Micah J. Leamer^b ; ^{s-mleamer1@math.unl.edu} ; Sean Sather-Wagstaff^a ; ^{sean.sather-wagstaff@ndsu.edu} ;
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2011
• 出版时间：October 2011
• 年：2011
• 卷：215
• 期：10
• 页码：2486-2503
• 全文大小：363 K

文摘

Let R be a commutative local noetherian ring, and let L and L^′ be R-modules. We investigate the properties of the functors and . For instance, we show the following:

(a) if L and L^′ are artinian, then is artinian, and is noetherian over the completion ;

(b) if L is artinian and L^′ is Matlis reflexive, then , , and are Matlis reflexive. Also, we study the vanishing behavior of these functors, and we include computations demonstrating the sharpness of our results.