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arXiv 1003.3974math.AC
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关于有限生成模的伪支撑与非Cohen-Macaulay轨迹

On pseudo supports and non Cohen-Macaulay locus of finitely generated modules

Nguyen Tu Cuong, Le Thanh Nhan, Nguyen Thi Kieu Nga

备注：
To appear in Journal of Algebra
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摘要：

设$(R,\m)$是一个Noether局部环，$M$是由$\dim M=d.$生成的$R$ -模，$i\geq 0$是一个整数.继M。Brodmann和R. Y.本文结合环\cite{BS1}的悬链性、$M$上的Serre条件以及$ H^{i-\dim (R/\p)}_{\p R_{\p}}(M_{\p})\neq 0.$中某些素理想$\p$的局部环$R/\p$的非混合性，研究了$M$的伪支撑和非Cohen-Macaulay轨迹.

英文摘要：

Let $(R,\m)$ be a Noetherian local ring and $M$ a finitely generated $R$-module with $\dim M=d.$ Let $i\geq 0$ be an integer. Following M. Brodmann and R. Y. Sharp \cite{BS1}, the $i$-th pseudo support of $M$ is the set of all prime ideals $\p$ of $R$ such that $ H^{i-\dim (R/\p)}_{\p R_{\p}}(M_{\p})\neq 0.$ In this paper, we study the pseudo supports and the non Cohen-Macaulay locus of $M$ in connections with the catenarity of the ring $R/\Ann_RM$, the Serre conditions on $M$, and the unmixedness of the local rings $R/\p$ for certain prime ideals $\p$ in $\Supp_R (M)$.

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