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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916301050&_mathId=si2.gif&_user=111111111&_pii=S0022404916301050&_rdoc=1&_issn=00224049&md5=82475f612d5ba5bcfc58d6160e76efe6" title="Click to view the MathML source">(A,m)class="mathContainer hidden">class="mathCode">$(A,\mathfrak{m})$ be a Noetherian local ring, let M be a finitely generated Cohen–Macaulay A  -module of dimension class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916301050&_mathId=si100.gif&_user=111111111&_pii=S0022404916301050&_rdoc=1&_issn=00224049&md5=dfc8f7ce8fb07459335aecd1c72ee39b" title="Click to view the MathML source">r≥2class="mathContainer hidden">class="mathCode">$r\ge 2$ and let I be an ideal of definition for M  . Set class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916301050&_mathId=si13.gif&_user=111111111&_pii=S0022404916301050&_rdoc=1&_issn=00224049&md5=b07862e00a53cf32dbbf1ac7286db07f" title="Click to view the MathML source">L^I(M)=⨁_n≥0M/Iⁿ⁺¹Mclass="mathContainer hidden">class="mathCode">$L^I(M)={⨁}_{n\ge 0}M/I^{n+1}M$. In part one of this paper we showed that class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916301050&_mathId=si5.gif&_user=111111111&_pii=S0022404916301050&_rdoc=1&_issn=00224049&md5=0effe47a0270678a31f86119521c2cc2" title="Click to view the MathML source">L^I(M)class="mathContainer hidden">class="mathCode">$L^I(M)$ is a module over class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916301050&_mathId=si6.gif&_user=111111111&_pii=S0022404916301050&_rdoc=1&_issn=00224049&md5=b21b780c69b1b5ee4643debfdd09f2b2" title="Click to view the MathML source">R(I)class="mathContainer hidden">class="mathCode">$\mathcal{R}(I)$, the Rees algebra of I   and we gave many applications of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916301050&_mathId=si5.gif&_user=111111111&_pii=S0022404916301050&_rdoc=1&_issn=00224049&md5=0effe47a0270678a31f86119521c2cc2" title="Click to view the MathML source">L^I(M)class="mathContainer hidden">class="mathCode">$L^I(M)$ to study the associated graded module, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916301050&_mathId=si152.gif&_user=111111111&_pii=S0022404916301050&_rdoc=1&_issn=00224049&md5=a1e57db211389be8de657d5719bb78d9" title="Click to view the MathML source">G_I(M)class="mathContainer hidden">class="mathCode">$G_I(M)$. 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.