Related papers: On generalized completion homology modules

Let $\frak a$ denote an ideal in a regular local (Noetherian) ring $R$ and let $N$ be a finitely generated $R$-module with support in $V(\frak a)$. The purpose of this paper is to show that all homomorphic images of the $R$-modules…

For a commutative Noetherian local ring we define and study the class of modules having reducible complexity, a class containing all modules of finite complete intersection dimension. Various properties of this class of modules are given,…

Let $R$ be a commutative Noetherian ring and let $n$ be a non-negative integer. In this article, by using the theory of Gorenstein dimensions, it is shown that whenever $R$ is a homomorphic image of a Noetherian Gorenstein ring, then the…

Let $R$ be a standard graded algebra over a field $k$, with irrelevant maximal ideal $\fm$, and $I$ a homogeneous $R$-ideal. We study the asymptotic vanishing behavior of the graded components of the local cohomology modules…

For finitely generated module $M$ over a local ring $R$, the conventional notions of complete intersection dimension $\cid_R M$ and Cohen-Macaulay dimension $\cmdim_R M$ do not extend to cover the case of infinitely generated modules. In…

Let $R$ be a commutative Noetherian ring with identity (not necessarily local) and $\frak a$ a proper ideal of $R$. We study the invariance of some classes of $\frak a$-relative Cohen-Macaulay modules under pure ring homomorphisms and ring…

Let R denote a commutative Noetherian ring and let I be an ideal of R such that H_i^I(R) = 0, for all integers i greater than or equal to 2. In this paper we shall prove some results concerning the homological properties of I.

Let $\Lambda$ be a finite-dimensional algebra over a fixed algebraically closed field $\mathbf{k}$ of arbitrary characteristic, and let $V$ be a finitely generated $\Lambda$-module. It follows from results previously obtained by F.M. Bleher…

Let $I$ denote an ideal of a local Gorenstein ring $(R, \mathfrak m)$. Then we show that the local cohomology module $H^c_I(R), c = \height I,$ is indecomposable if and only if $V(I_d)$ is connected in codimension one. Here $I_d$ denotes…

Let $I$ be an ideal of height $d$ in a regular local ring $(R,m,k=R/m)$ of dimension $n$ and let $\Omega$ denote the canonical module of $R/I$. In this paper we first prove the equivalence of the following: the non-vanishing of the edge…

Let $R$ denote a commutative Noetherian ring. Brodmann et al. defined and studied the concept of the local-global principle for annihilation of local cohomology modules at level $r\in\mathbb{N}$ for the ideals $\frak a$ and $\frak b$ of…

Suppose that k is a field of characteristic zero, X is an r by s matrix of indeterminates, where r \leq s, and R = k[X] is the polynomial ring over k in the entries of X. We study the local cohomology modules H^i_I(R), where I is the ideal…

We study homomorphisms between quantized generalized Verma modules $M(V_{\Lambda})\stackrel{\phi_{\Lambda,\Lambda_1}}{\rightarrow}M(V_{\Lambda_1})$ for ${\mathcal U}_q(su(n,n))$. There is a natural notion of degree for such maps, and if the…

Let $A$ be a regular domain containing a field $K$ of characteristic zero, $G$ be a finite subgroup of the group of automorphisms of $A$ and $B=A^G$ be the ring of invariants of $G$. Let $S= A[X_1,\ldots, X_m]$ and $R= B[X_1, \ldots, X_m]$…

Let R be a local complete ring. For an R-module M the canonical ring map R\to End_R(M) is in general neither injective nor surjective; we show that it is bijective for every local cohomology module M := H^h_I(R) if H^l_I(R) = 0 for every…

Assume that $R = \bigoplus_{i\in \mathbb{N}_{0}} R_{i}$ is a homogeneous graded Noetherian ring, and that $M$ is a $ \mathbb{Z}$--graded $R$--module, where $ \mathbb{N}_{0}$ (resp. $ \mathbb{Z}$) denote the set all non--negative integers…

Let $(R,m)$ be a local Noetherian ring, let $I\subset R$ be any ideal and let $M$ be a finitely generated $R$-module. In 1990 Craig Huneke conjectured that the local cohomology modules $H^i_I(M)$ have finitely many associated primes for all…

We investigate stable homology of modules over a commutative noetherian ring $R$ with respect to a semidualzing module $C$, and give some vanishing results that improve/extend the known results. As a consequence, we show that the balance of…

Let $\mathfrak{a}$ be an ideal of a commutative Noetherian ring $R$ and $M$ a finitely generated $R$-module. In this paper we proved that if $\operatorname{Supp}\mathfrak{F}_\mathfrak{a}^i(M)$ is finite for all $i<t$, then so is…

Let (R,m) be a local, complete ring, X an artinian R-module of Noetherian dimension d; let x_1,...,x_d\in m be such that 0:_X (x_1,...,x_d)R has finite length. Then H^x_d(X) is a finite R-module, providing a positive answer to a question…