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تسجيل مستخدم جديدRatliff-Rush Filtration, regularity and depth of Higher Associated graded modules: Part II
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تأليف
Tony J. Puthenpurakal
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Let $(A,m)$ be a Noetherian local ring, let $M$ be a finitely generated CM $A$-module of dimension $r geq 2$ and let $I$ be an ideal of definition for $M$. Set $L^I(M) = bigoplus_{ngeq 0}M/I^{n+1}M$. In part one of this paper we showed that $L^I(M)$ is a module over $R$, the Rees algebra of $I$ and we gave many applications of $L^I(M)$ to study the associated graded module, $G_I(M)$. In this paper we give many further applications of our technique; most notable is a reformulation of a classical result due to Narita in terms of the Ratliff-Rush filtration. This reformulation can be extended to all dimensions $geq 2$.
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Let $A$ be a commutative Noetherian ring containing a field $K$ of characteristic zero and let $R= A[X_1, ldots, X_m]$. Consider $R$ as standard graded with $deg A=0$ and $deg X_i=1$ for all $i$. We present a few results about the behavior of the gra
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