Homology of artinian and mini-max modules, II
| Autor: | Micah J. Leamer, Bethany Kubik, Sean Sather-Wagstaff |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Noetherian
Discrete mathematics Algebra and Number Theory Mathematics::Commutative Algebra Betti number 010102 general mathematics Mathematics::Rings and Algebras 010103 numerical & computational mathematics Commutative ring Homology (mathematics) Mathematics - Commutative Algebra Commutative Algebra (math.AC) 01 natural sciences Primary: 13D07 13E10. Secondary: 13B35 13E05 Tensor product Mathematics::K-Theory and Homology FOS: Mathematics Bass number 0101 mathematics Mathematics::Representation Theory Mathematics |
| DOI: | 10.48550/arxiv.1208.5534 |
| Popis: | 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). Comment: 35 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|