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