An independent result for attached primes of certain Tor-modules
Bull. Korean Math. Soc. 2015 Vol. 52, No. 2, 531-540
Published online March 31, 2015
Pham Huu Khanh
Tay Nguyen University
Abstract : Let $(R,\m)$ be a Noetherian local ring, $I$ an ideal of $R$, and $A$ an Artinian $R$-module. Let $k\ge 0$ be an integer and $r=\Width_{>k}(I,A)$ the supremum of length of $A$-cosequence in dimension $>k$ in $I$ defined by Nhan-Hoang \cite{NhHo}. It is shown that for all $t\le r$ the sets $$(\overset t{\bigcup\limits_{i=0}}\Att_R(\Tor_i^R(R/I^n, A)))_{\ge k}\text{ and }$$ $$(\overset t{\bigcup\limits_{i=0}}\Att_R(\Tor_i^R(R/(a_1^{n_1},\ldots,a_l^{n_l}), A)))_{\ge k}$$ are independent of the choice of $n, n_1,\ldots,n_l$ for any system of generators $(a_1,\ldots, a_l)$ of $I$.
Keywords : asymptotic stability, attached prime, Tor-module, $A$-cosequence in dimension $>k$, width in dimension $>k$
MSC numbers : 13D45, 13E05
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