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چکیده
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Let $(R,\frak{m})$ be a $d$-dimensional Cohen-Macaulay local ring, $I$ an $\frak{m}$-primary ideal and $J$ a minimal reduction ideal of $I$. If $M$ is a maximal Cohen-Macaulay $R$-module then, for $n$ sufficiently large and $1\leq i\leq d$, the length of the modules $\Ext^i_R(R/J,M/I^nM)$ and $\Tor_i^R(R/J,M/I^nM)$ are polynomial of degree $d-1$. Moreover, we show that $\deg\beta_i^R(M/I^nM)=\deg\mu^i_R(M/I^nM)=d-1$, where $\beta_i^R(-)$ and $\mu^i_R(-)$ are the ith Betti number and the ith Bass number, respectively.
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