ﻻ يوجد ملخص باللغة العربية
Let $(A,mathfrak{m})$ be an analytically unramified formally equidimensional Noetherian local ring with $ depth A geq 2$. Let $I$ be an $mathfrak{m}$-primary ideal and set $I^*$ to be the integral closure of $I$. Set $G^*(I) = bigoplus_{ngeq 0} (I^n)^*/(I^{n+1})^*$ be the associated graded ring of the integral closure filtration of $I$. We prove that $ depth G^*(I^n) geq 2$ for all $n gg 0$. As an application we prove that if $A$ is also an excellent normal domain containing an algebraically closed field isomorphic to $A/m$ then there exists $s_0$ such that for all $s geq s_0$ and $J$ is an integrally closed ideal emph{strictly} containing $(mathfrak{m}^s)^*$ then we have a strict inequality $mu(J) < mu((mathfrak{m}^s)^*)$ (here $mu(J)$ is the number of minimal generators of $J$).
The Qth-power algorithm for computing structured global presentations of integral closures of affine domains over finite fields is modified to compute structured presentations of integral closures of ideals in affine domains over finite fields relati
The purpose of this note is to revisit the results of arXiv:1407.4324 from a slightly different perspective, outlining how, if the integral closures of a finite set of prime ideals abide the expected convexity patterns, then the existence of a peculi
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)
In this article, we study the regularity of integral closure of powers of edge ideals. We obtain a lower bound for the regularity of integral closure of powers of edge ideals in terms of induced matching number of graphs. We prove that the regularity
Let $(A,mathfrak{m})$ be a local complete intersection ring and let $I$ be an ideal in $A$. Let $M, N$ be finitely generated $A$-modules. Then for $l = 0,1$, the values $depth Ext^{2i+l}_A(M, N/I^nN)$ become independent of $i, n$ for $i,n gg 0$. We