Related papers: On Coefficient ideals

We generalize a Brian\c{c}on-Skoda type theorem first studied by Aberbach and Huneke. With some conditions on a regular local ring $(R,\m)$ containing a field, and an ideal $I$ of $R$ with analytic spread $\ell$ and a minimal reduction $J$,…

In this article, we prove that if $R\to S$ is a homomorphism of Noetherian rings that splits, then for every $i\geq 0$ and ideal $I\subset R$, $\Ass_R H^i_I(R)$ is finite when $\Ass_S H^i_{IS}(S)$ is finite. In addition, if $S$ is a…

Let $A$ be a non Gorenstein Cohen Macaulay ring of dimension $d\geq 1$, $I$ an ideal of $A$, and suppose $\omega_A$ is a canonical $A$-module. Set $$r(I,\omega_A) = \bigcup_{n \geq 0} (I^{n+1} \omega_A : I^{n} \omega_A) \subseteq A .$$ We…

Let $(A,\mathfrak{m})$ be an excellent Henselian Cohen-Macaulay local ring of finite representation type. If the AR-quiver of $A$ is known then by a result of Auslander and Reiten one can explicity compute $G(A)$ the Grothendieck group of…

Inspired by the works in linkage theory of ideals, we define the concept of linkage of ideals over a module. Several known theorems in linkage theory are improved or recovered by new approaches. Specially, we make some extensions and…

The overall goal is to approach the Cohen--Macaulay property of the special fiber $\mathcal{F}(I)$ of an equigenerated homogeneous ideal $I$ in a standard graded ring over an infinite field. When the ground ring is assumed to be local, the…

Let $k$ be a field of characteristic zero, and $R=k[x_1, \ldots, x_d]$ with $d \geq 3$ be a polynomial ring in $d$ variables. Let $\m=(x_1, \ldots, x_d)$ be the homogeneous maximal ideal of $R$. Let $\mathcal{K}$ be the kernel of the…

Let $R$ be a Noetherian ring, $I$ and $J$ two ideals of $R$ and $t$ an integer. Let $S$ be the class of Artinian $R$-modules, or the class of all $R$-modules $N$ with $\dim_RN\leq k$, where $k$ is an integer. It is proved that $\inf\{i:…

Two formulas for the multiplicity of the fiber cone $F(I)=\oplus_{n=0}^{\infty} I^n/\m I^n$ of an $\m$-primary ideal of a $d$-dimensional Cohen-Macaulay local ring $(R,\m)$ are derived in terms of the mixed multiplicity $e_{d-1}(\m | I),$…

This paper considers the following conjecture: If $R$ is an unmixed, equidimensional local ring that is a homomorphic image of a Cohen-Macaulay local ring, then for any ideal $J$ generated by a system of parameters, the Chern coefficient…

Let $H$ be a semisimple Hopf algebra, and let $R$ be a noetherian left $H$-module algebra. If $R/R^H$ is a right $H^*$-dense Galois extension, then the invariant subalgebra $R^H$ will inherit the AS-Cohen-Macaulay property from $R$ under…

Let (A, m) be a Noetherian local ring and N a parameter module in F=A^r and M=N:_F m the socle module of N. In this paper, we shall prove that the module M=N:_F m has a reduction number at most one and hence its Rees algebra R(M) is…

In this paper we give several classes of Non-Gorenstein local rings $A$ which satisfy the property that $\text{Ext}^i_A(M, A) = 0$ for $i \gg 0$ then $\text{projdim}_A M$ is finite. We also show that if $\text{injdim}_A M = \infty$ then…

We extend the Boutet de Monvel Toeplitz index theorem to complex manifold with isolated singularities following the relative $K$-homology theory of Baum, Douglas, and Taylor for manifold with boundary. We apply this index theorem to study…

In this paper, we investigate the relationship between the index of reducibility and Chern coefficients for primary ideals. As an application, we give characterizations of a Cohen-Macaulay ring in terms of its type, irreducible…

In this paper we investigate some properties of Rees algebras of divisorial filtrations and their analytic spread. A classical theorem of McAdam shows that the analytic spread of an ideal $I$ in a formally equidimensional local ring is…

In this paper we show that a large class of one-dimensional Cohen-Macaulay local rings $(A,\mathfrak{m})$ has the property that if $M$ is a maximal Cohen-Macaulay $A$-module then the Hilbert function of $M$ ( with respect to $\mathfrak{m}$)…

Given a one-dimensional Cohen-Macaulay local ring $(R,\mathfrak{m},k)$, we prove that it is almost Gorenstein if and only if $\mathfrak{m}$ is a canonical module of the ring $\mathfrak{m}:\mathfrak{m}$. Then, we generalize this result by…

In the first part of the paper we answer (positively) a question raised by the first author which has to do with some sort of rigity of the tail of resolution of an ideal. Let $I$ be a homogeneous ideal in a polynomial ring over a field of…

Consider a rational projective plane curve C parameterized by three homogeneous forms h1,h2,h3 of the same degree d in the polynomial ring R=k[x,y] over the field k. Extracting a common factor, we may harmlessly assume that the ideal…