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 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∨).
Original language | English (US) |
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Pages (from-to) | 229-272 |
Number of pages | 44 |
Journal | Journal of Algebra |
Volume | 403 |
DOIs | |
State | Published - Feb 1 2014 |
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 by a GAANN grant from the Department of Education. Sean Sather-Wagstaff was supported by a grant from the NSA .
Keywords
- Artinian
- Bass number
- Betti number
- Ext
- Hom
- Matlis duality
- Mini-max
- Noetherian
- Primary
- Secondary
- Tensor product
- Tor