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On Shifted Principles for Attached Primes of the Top Local Cohomology Modules
Tran Do Minh Chau
,
Nguyen Thi Kieu Nga
,
Le Thanh Nhan
Abstract
Let $(R, \mathfrak{m})$ be a Noetherian local ring, let $I$ be an ideal of $R$, and let $M$ be a finitely generated $R$-module with $d=\dim(M)$. In this paper, we establish shifted principles under localization and completion for attached primes of the top local cohomology module $H^d_I(M)$. We characterize the catenarity, the weak going-up property, and the strong Lichstenbaum-Hartshorne vanishing property of the base ring $R$ in terms of these shifted principles of the top local cohomology modules.