Let $\frak a$ denote an ideal in a regular local (Noetherian) ring $R$ andlet $N$ be a finitely generated $R$-module with support in $V(\frak a)$. Thepurpose of this paper is to show that all homomorphic images of the $R$-modules$\Ext^j_R(N, H^i_{\frak a}(R))$ have only finitely many associated primes, forall $i, j\geq 0$, whenever $\dim R \leq4$ or $\dim R/ \frak a \leq 3$ and $R$contains a field. In addition, we show that if $\dim R=5$ and $R$ contains afield, then the $R$-modules $\Ext^j_R(N, H^i_{\frak a}(R))$ have only finitelymany associated primes, for all $i, j\geq 0$.
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机译:令$ \ frak a $表示常规局部(Noetherian)环$ R $中的理想情况,而让$ N $为有限生成的$ R $模块,并在$ V(\ frak a)$中提供支持。本文的目的是证明$ R $ -modules $ \ Ext ^ j_R(N,H ^ i _ {\ frak a}(R))$的所有同构图像只有有限多个关联素数,所有$ i, j \ geq 0 $,每当$ \ dim R \ leq4 $或$ \ dim R / \ frak一个\ leq 3 $和$ R $包含一个字段时。此外,我们证明如果$ \ dim R = 5 $并且$ R $包含一个字段,则$ R $-模块$ \ Ext ^ j_R(N,H ^ i _ {\ frak a}(R))$具有对于所有$ i,仅\ j \ geq 0 $有限地有多个质数。
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