An independent result for attached primes of certain Tor-modules

摘要

Let $(R,m)$ be a Noetherian local ring, $I$ an ideal of $R$, and $A$ an Artinian $R$-module. Let $kge 0$ 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 $tle r$ the sets $$(overset t{igcuplimits_{i=0}}Att_R(Tor_i^R(R/I^n, A)))_{ge k}ext{ and }$$ $$(overset t{igcuplimits_{i=0}}Att_R(Tor_i^R(R/(a_1^{n_1},ldots,a_l^{n_l}), A)))_{ge k}$$ are independent of the choice of $n, n_1,ldots,n_l$ for any system of generators $(a_1,ldots, a_l)$ of $I$.