On The Finiteness and Stability of Certain Sets of Associated Prime Ideals of Local Cohomology Modules
| Autor: | Nguyen Van Hoang, Nguyen Tu Cuong |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Communications in Algebra. 42:1757-1768 |
| ISSN: | 1532-4125 0092-7872 1527-1536 |
| DOI: | 10.1080/00927872.2012.749262 |
| Popis: | Let $(R,\frak{m})$ be a Noetherian local ring, $I$ an ideal of $R$ and $N$ a finitely generated $R$-module. Let $k{\ge}-1$ be an integer and $ r=\depth_k(I,N)$ the length of a maximal $N$-sequence in dimension $>k$ in $I$ defined by M. Brodmann and L. T. Nhan ({Comm. Algebra, 36 (2008), 1527-1536). For a subset $S\subseteq \Spec R$ we set $S_{{\ge}k}={\p\in S\mid\dim(R/\p){\ge}k}$. We first prove in this paper that $\Ass_R(H^j_I(N))_{\ge k}$ is a finite set for all $j{\le}r$}. Let $\fN=\oplus_{n\ge 0}N_n$ be a finitely generated graded $\fR$-module, where $\fR$ is a finitely generated standard graded algebra over $R_0=R$. Let $r$ be the eventual value of $\depth_k(I,N_n)$. Then our second result says that for all $l{\le}r$ the sets $\bigcup_{j{\le}l}\Ass_R(H^j_I(N_n))_{{\ge}k}$ are stable for large $n$. To appear in Communication in Algebra |
| Databáze: | OpenAIRE |
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