标题： 通过几乎阶乘环的性质，理想局部上同调模的关联素理想的有限性 显示英文标题

标题： Finiteness of the set of associated primes for local cohomology modules of ideals via properties of almost factorial rings

摘要： 我们通过比较 $H_I^{d+1}(J)$ 和 $H_I^d(R/J)$来研究局部上同调模 $H_I^{i}(J)$对于由 $R$-序列生成的理想 $J$的相关素理想的有限性，其中 $d = \mathrm{depth}_I(R)$。几乎阶乘环的性质在实现这种比较中起着关键作用。 在适当条件下，我们证明$\mathrm{Ass} H_I^{d+1}(J)$的有限性等价于$\mathrm{Ass} H_I^d(R/J)$的有限性。 此外，我们给出了一些条件，使得对于所有$i$，$\mathrm{Ass} H_I^i(J)$的有限性成立。 显示英文摘要

摘要： We investigate the finiteness of the set of associated primes for local cohomology modules $H_I^{i}(J)$ of an ideal $J$ generated by an $R$-sequence, through the comparison of $H_I^{d+1}(J)$ and $H_I^d(R/J)$, where $d = \mathrm{depth}_I(R)$. The properties of almost factorial rings play a key role in enabling this comparison. Under suitable conditions, we prove that the finiteness of $\mathrm{Ass} H_I^{d+1}(J)$ is equivalent to that of $\mathrm{Ass} H_I^d(R/J)$. Moreover, we give a few conditions under which the finiteness of $\mathrm{Ass} H_I^i(J)$ holds for all $i$.