Ratliff-Rush filtration, regularity and depth of higher associated graded modules. Part II

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• 作者：Tony J. Puthenpurakal¹ ; ^{tputhen@math.iitb.ac.in" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Primary ; 13A30 ; secondary ; 13D40 ; 13D07 ; 13D45
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：221
• 期：3
• 页码：611-631
• 全文大小：445 K

文摘

Let (A,m)$(A,\mathfrak{m})$ be a Noetherian local ring, let M be a finitely generated Cohen–Macaulay A  -module of dimension r≥2$r\ge 2$ and let I be an ideal of definition for M  . Set L^I(M)=⨁_n≥0M/Iⁿ⁺¹M$L^I(M)={⨁}_{n\ge 0}M/I^{n+1}M$. In part one of this paper we showed that L^I(M)$L^I(M)$ is a module over R(I)$\mathcal{R}(I)$, the Rees algebra of I   and we gave many applications of L^I(M)$L^I(M)$ to study the associated graded module, G_I(M)$G_I(M)$. In this paper we give many further applications of our technique; most notable is a complete characterization of good behavior of the Ratliff–Rush filtration modulo a superficial element.