挠函子的二元Hilbert函数
Bivariate Hilbert Functions for the Torsion Functor
摘要：
设$(R,P)$是交换的局部Noether环，$I$，$J$理想，$M$和$N$是生成的$R$ -模.假设$J + ann_R M + ann_R N$是$P$ -primary。本文的主要结果是定理6，它给出了$\t_i(M/I^nM,N/J^mN)$的长度与多项式一致的充要条件，对于$m$，$n \gg 0$ .作为推论，它表明，$\t_i(M/I^nM,N/I^nN))$的长度总是同意在$n$的多项式，$n \gg 0$，提供$I + ann_R M + ann_R N$是$P$ -小学。
英文摘要：
Let $(R,P)$ be a commutative, local Noetherian ring, $I$, $J$ ideals, $M$ and $N$ finitely generated $R$-modules. Suppose $J + ann_R M + ann_R N$ is $P$-primary. The main result of this paper is Theorem 6, which gives necessary and sufficient conditions for the length of $\t_i(M/I^nM,N/J^mN)$, to agree with a polynomial, for $m$, $n \gg 0$. As a corollary, it is shown that the length of $\t_i(M/I^nM,N/I^nN))$ always agrees with a polynomial in $n$, for $n \gg 0$, provided $I + ann_R M + ann_R N$ is $P$-primary.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
