Homology of artinian and mini-max modules, II
Commutative Algebra
2012-08-29 v1
Abstract
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 Ext^i_R(L,L') and Tor_i^R(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 Ext^i_R(M,M'), Ext^i_R(M',M), and Tor_i^R(M,M') are Matlis reflexive over R for all i\geq 0 and that Ext^i_R(M,M')^\vee\cong Tor_i^R(M,M'^\vee) and Ext^i_R(M',M)^\vee\cong Tor_i^R(M',M^\vee).
Keywords
Cite
@article{arxiv.1208.5534,
title = {Homology of artinian and mini-max modules, II},
author = {Bethany Kubik and Micah Leamer and Sean Sather-Wagstaff},
journal= {arXiv preprint arXiv:1208.5534},
year = {2012}
}
Comments
35 pages