Related papers: The locally nilradical for modules over commutativ…

Through a study of torsion functors of local cohomology modules we improve some non-finiteness results on the top non-zero local cohomology modules with respect to an ideal.

In this paper we study homological dimensions of finitely generated modules over commutative Noetherian local rings, called reducing homological dimensions. We obtain new characterizations of Gorenstein and complete intersection local rings…

Let A be a noetherian AS regular Koszul quiver algebra (if A is commutative, it is essentially a polynomial ring), and grA the category of finitely generated graded left A-modules. Following Jorgensen, we define the Castelnuovo-Mumford…

We define a functor $\rr^\ast$ from the category of positively determined modules to the category of squarefree modules which plays the role of passing from a monomial ideal to its radical. By using this functor, we generalize several…

Let $R$ be a commutative Noetherian ring and $\mathfrak{a}$ be an ideal of $R$. Suppose $M$ is a finitely generated $R$-module and $N$ is an Artinian $R$-module. We define the concept of filter coregular sequence to determine the infimum of…

Let $R$ be a commutative Noetherian ring. We introduce the notion of localization functors $\lambda^W$ with cosupports in arbitrary subsets $W$ of $\text{Spec}\, R$; it is a common generalization of localizations with respect to…

We introduce and investigate using Hilbert modules the properties of the {\em Fourier algebra} $A(G)$ for a locally compact groupoid $G$. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This…

Let $(A,\mathfrak{m})$ be a hypersurface local ring of dimension $d \geq 1$, $N$ a perfect $A$-module and let $I$ be an ideal in $A$ with $\ell(N/IN)$ finite. We show that there is a integer $r_I \geq -1$ (depending only on $I$ and $N$)…

Let $\mathfrak{a}$ be an ideal of a commutative noetherian (not necessarily local) ring $R$. In the case $\cd(\mathfrak{a},R)\leq 1$, we show that the subcategory of $\mathfrak{a}$-cofinite $R$-modules is abelian. Using this and the…

Let $\mathfrak{a}$ be an ideal of local ring $(R,\mathfrak{m})$ and $M$ a finitely generated $R$-module and $n\in\Bbb N$. It is shown that some results concerning cominimaxness of formal local cohomology modules.

Global Weyl modules for generalized loop algebras $\lie g\tensor A$, where $\lie g$ is a simple finite dimensional Lie algebra and A is a commutative associative algebra were defined, for any dominant integral weight $\lambda$, by…

Let R be a commutative Noetherian ring, I and J ideals of R and M a finitely generated R-module. Let F be a covariant R-linear functor from the category of finitely generated R-modules to itself. We first show that if F is coherent, then…

In this paper, we develop general machinery for computing the classifying ring $L^A$ of one-dimensional formal $A$-modules, for various commutative rings $A$. We then apply the machinery to obtain calculations of $L^A$ for various number…

Let $A$ be an associative non-positive differential graded ring. In this paper we make a detailed study of a category $\operatorname{\mathsf{Inj}}(A)$ of left DG-modules over $A$ which generalizes the category of injective modules over a…

Let $A$ be a Noetherian domain and $R$ be a finitely generated $A$-algebra. We study several features regarding the generic freeness over $A$ of an $R$-module. For an ideal $I \subset R$, we show that the local cohomology modules ${\rm…

We study a class of non-local functionals that was introduced by Brezis--Seeger--Van Schaftingen--Yung, and can be used to characterize the total variation of functions. We establish the $\Gamma$-limit of these functionals with respect to…

Let $R=k[x_1,..., x_n]$ be a polynomial ring over a field $k$ of characteristic $p>0,$ let $\m=(x_1,..., x_n)$ be the maximal ideal generated by the variables, let $^*E$ be the naturally graded injective hull of $R/\m$ and let $^*E(n)$ be…

We prove a compactness result with respect to $\Gamma$-convergence for a class of integral functionals which are expressed as a sum of a local and a non-local term. The main feature is that, under our hypotheses, the local part of the…

Let $G$ be a groupoid acting on a set $X$ and let $R$ be a $G$-graded ring with graded local units. We study the main properties of the category $gr-(R,G,X)$ of $X$-graded $R$-modules and adjoint functors between categories of this kind. We…

We define global and local Weyl modules for Lie superalgebras of the form $\mathfrak{g} \otimes A$, where $A$ is an associative commutative unital $\mathbb{C}$-algebra and $\mathfrak{g}$ is a basic Lie superalgebra or $\mathfrak{sl}(n,n)$,…