Homology of artinian and mini-max modules, II

Let R be a commutative ring, and let L and L′ be R-modules. We investigate finiteness conditions (e.g., noetherian, artinian, mini-max, Matlis reflexive) of the modules ExtRi(L,L′) and ToriR(L,L′) when L and L′ satisfy combinations of these finiteness conditions. For instance, if R is noetherian, then given R-modules M and M′ such that M is Matlis reflexive and M′ is mini-max (e.g., noetherian or artinian), we prove that ExtRi(M,M′), ExtRi(M′,M), and ToriR(M,M′) are Matlis reflexive over R for all i≥0 and that ExtRi(M,M′)∨≅ToriR(M,M′∨) and ExtRi(M′,M)∨≅ToriR(M′,M∨).