Local Cohomology Modules and their Properties
Autor: | Masoumeh Hasanzad, Jafar A'zami |
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Rok vydání: | 2021 |
Předmět: |
Noetherian
Functor Mathematics::Commutative Algebra Cofiniteness General Mathematics 010102 general mathematics Dimension (graph theory) 0211 other engineering and technologies Local ring 021107 urban & regional planning 02 engineering and technology Local cohomology 01 natural sciences Combinatorics Ideal (ring theory) 0101 mathematics Algebra over a field Mathematics |
Zdroj: | Ukrainian Mathematical Journal. 73:311-319 |
ISSN: | 1573-9376 0041-5995 |
DOI: | 10.1007/s11253-021-01924-z |
Popis: | Let (R,m) be a complete Noetherian local ring and let M be a generalized Cohen–Macaulay R-module of dimension d ≥ 2. We show that $$ D\left({H}_m^d\left(D\left({H}_m^d\left({D}_m(M)\right)\right)\right)\right)\approx {D}_m(M), $$ where D = Hom(−,E) and Dm(−) is the ideal transform functor. In addition, by assuming that I is a proper ideal of a local ring R, we obtain some results on finiteness of the Bass numbers, cofiniteness, and cominimaxness of the local cohomology modules with respect to I. |
Databáze: | OpenAIRE |
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