Name
Abstract | ||
|---|---|---|
Let I be an ideal of a local commutative noetherian ring (\(R, {{\mathfrak {m}}}\)) and M a finitely generated R-module. We study some properties of the top formal local cohomology module \({\mathcal {F}}^l_I(M)=\mathop {\varprojlim }H^l_{{{\mathfrak {m}}}}(M{/}I^tM)\) with \(l=\mathrm {dim}M{/}I M\). In particular, we show that, in the case \(M \ne IM\), \({\mathcal {F}}^l_I(M)\) is artinian if and only if \(l>\mathrm {dim}{\overline{M}}/I{\overline{M}}\) where \({\overline{M}}=M/ H^0_I(M)\). As a consequence, we have \( \mathrm {dim}{\overline{M}}/I{\overline{M}}=\sup \{i \in {\mathbb {Z}}\mid {\mathcal {F}}^i_I(M) \text { is not artinian}\},\) provided that \({\overline{M}} \ne I{\overline{M}}\). |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1007/s10998-018-0256-x | Periodica Mathematica Hungarica |
Keywords | Field | DocType |
Formal local cohomology,Minimax module,Finitely generated module,13D45 | Combinatorics,Noetherian ring,Finitely-generated abelian group,Mathematical analysis,Finitely-generated module,Local cohomology,Mathematics | Journal |
Volume | Issue | ISSN |
79 | 1 | 1588-2829 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tran Tuan Nam | 1 | 1 | 1.64 |
| Tu Hoang Huy Nguyen | 2 | 0 | 0.34 |
| Nguyen Minh Tri | 3 | 28 | 4.62 |