A splitting theorem for local cohomology and its applications

DOI10.1016/j.jalgebra.2010.09.017zbMath1227.13012arXiv1009.3531OpenAlexW2962828416MaRDI QIDQ716481

Pham Hung Quy, Nguyen Tu Cuong

Publication date: 22 September 2011

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.3531

zbMATH Keywords

split exact sequenceslocal cohomologygeneralized Cohen-Macaulay modulesgroup of extensions

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Local cohomology and commutative rings (13D45)

Related Items (17)

On the vanishing of local cohomology of the absolute integral closure in positive characteristic ⋮ Some splitting theorems for extension and torsion functors of local cohomology modules ⋮ Reducibility of parameter ideals in low powers of the maximal ideal ⋮ Modules whose finiteness dimensions coincide with their cohomological dimensions ⋮ On the uniform bound of the index of reducibility of parameter ideals of a module whose polynomial type is at most one ⋮ A uniform bound of reducibility index of good parameter ideals for certain class of modules ⋮ Tight closure of parameter ideals in local rings \(F\)-rational on the punctured spectrum ⋮ On the Frobenius closure of parameter ideals in local rings F-injective on the punctured spectrum ⋮ On the uniform bound of reducibility index of parameter ideals of idealizations ⋮ The index of reducibility of powers of a standard parameter ideal ⋮ On the index of reducibility of parameter ideals: the stable and limit values ⋮ \(F\)-injectivity and Frobenius closure of ideals in Noetherian rings of characteristic \(p>0\) ⋮ Attached primes of local cohomology modules under localization and completion ⋮ On Hilbert coefficients and sequentially Cohen-Macaulay rings ⋮ Some splitting theorems for local cohomology modules with respect to a pair of ideals ⋮ A Remark on the Finiteness Dimension ⋮ On the index of reducibility in Noetherian modules

Cites Work

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• Asymptotic behavior of parameter ideals in generalized Cohen-Macaulay modules
• Finiteness properties of local cohomology modules (an application of \(D\)- modules to commutative algebra)
• An example of an infinite set of associated primes of a local cohomology module
• The equality \(I^2=QI\) in Buchsbaum rings
• Bass Numbers of Local Cohomology Modules
• A finiteness result for associated primes of local cohomology modules
• ON THE FINITENESS PROPERTIES OF THE GENERALIZED LOCAL COHOMOLOGY MODULES

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