Homology of artinian and Matlis reflexive modules, I

Bethany Kubik, Micah J. Leamer, Sean Sather-Wagstaff

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Let R be a commutative local noetherian ring, and let L and L' be R-modules. We investigate the properties of the functors ToriR(L,-) and ExtRi(L,-). For instance, we show the following: (a)if L and L' are artinian, then ToriR(L,L') is artinian, and ExtRi(L,L') is noetherian over the completion R̂;(b)if L is artinian and L' is Matlis reflexive, then ExtRi(L,L'), ExtRi(L',L), and ToriR(L,L') are Matlis reflexive. Also, we study the vanishing behavior of these functors, and we include computations demonstrating the sharpness of our results.

Original languageEnglish (US)
Pages (from-to)2486-2503
Number of pages18
JournalJournal of Pure and Applied Algebra
Volume215
Issue number10
DOIs
StatePublished - Oct 2011

Bibliographical note

Funding Information:
✩ This material is based on work supported by North Dakota EPSCoR and National Science Foundation Grant EPS-0814442. Micah Leamer was supported

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