Related papers: Local Derivations of Finitary Incidence Algebras

There are many possible definitions of derivatives, here we present some and present one that we have called generalized that allows us to put some of the others as a particular case of this but, what interests us is to determine that there…

Let A be a commutative Noetherian ring of dimension d and let P be a projective R=A[X_1,\ldots,X_l,Y_1,\ldots,Y_m,\frac {1}{f_1\ldots f_m}]-module of rank r\geq max {2,dim A+1, where f_i\in A[Y_i]. Then (i) \EL^1(R\op P) acts transitively…

We study the set $\mathcal{L}_{F}$ of all $F$-vector spaces $L(P)$ where $P$ is monic and splits over $F$ and $L(Q)$ denotes the set of linear recurrence sequences over $F$ with characteristic polynomial $Q$. We show that $\mathcal{L}_{F}$…

We introduce the notion of finitary computable reducibility on equivalence relations on the natural numbers. This is a weakening of the usual notion of computable reducibility, and we show it to be distinct in several ways. In particular,…

We consider boundary value problems with Riemann-Liouville fractional derivatives of order $s\in (1, 2)$ with non-constant diffusion and reaction coefficients. A variational formulation is derived and analyzed leading to the well-posedness…

Let $\mathbb{K}$ be a field, $R$ be an associative and commutative $\mathbb{K}$-algebra and $L$ be a Lie algebra over $\mathbb{K}$. We give some descriptions of injections from $L$ to Lie algebra of $\mathbb{K}$-derivations of $R$ in the…

In this paper we are concerned with the finiteness property of Ext-indices of several ring extensions. In this direction, we introduce some conjectures and discuss the relationship of them. Also we give affirmative answers to these…

The paper is devoted to local derivations on the algebra $S(\mathcal{M},\tau)$ of $\tau$-measurable operators affiliated with a von Neumann algebra $\mathcal{M}$ and a faithful normal semi-finite trace $\tau.$ We prove that every local…

Structural properties of unitary groups over local, not necessarily commutative, rings are developed, with applications to the computation of the orders of these groups (when finite) and to the degrees of the irreducible constituents of the…

A finite projective plane, or more generally a finite linear space, has an associated incidence complex that gives rise to two natural algebras: the Stanley-Reisner ring $R/I_\Lambda$ and the inverse system algebra $R/I_\Delta$. We give a…

Let $R$ be a ring with identity and $I(X,R)$ be the incidence algebra of a locally finite partially ordered set $X$ over $R.$ In this paper, we compute the socle and the singular ideal of the incidence ring for some $X$ in terms of the…

Let $K$ be an unramified $p$-adic local field and let $W$ be the ring of integers of $K$. Let $(X,S)/W$ be a smooth proper scheme together with a simple normal crossings divisor and fix positive integers $r$ and $f$. We show that the set of…

In this paper we prove that if $G(R)=G_\pi (\Phi,R)$ $(E(R)=E_{\pi}(\Phi, R))$ is an (elementary) Chevalley group of rank $> 1$, $R$ is a local ring (with $\frac{1}{2}$ for the root systems ${\mathbf A}_2, {\mathbf B}_l, {\mathbf C}_l,…

We prove some regularity results for a priori bounded local minimizers of non-autonomous integral functionals of the form $$\mathcal{F}(v,\Omega)=\int_\Omega F(x,Dv)dx,$$ under the constraint $v \ge \psi$ a.e. in $\Omega$, where $\psi$ is a…

In this paper, we prove that every local derivation on Witt algebras $W_n, W_n^+$ or $W_n^{++} $ is a derivation for any $n\in\mathbb{N}$. As a consequence, we obtain that every local derivation on a centerless generalized Virasoro algebra…

In the present paper we prove that every 2-local derivation on a semi-finite von Neumann algebra is a derivation.

We resolve a conjecture of Li and Ramos that relates the regularity of an FI-module to its local cohomology groups. This is an analogue of the familiar relationship between regularity and local cohomology in commutative algebra.

Let n be a positive integer, F be a non-Archimedean locally compact field of odd residue characteristic p and G be an inner form of GL(2n,F). This is a group of the form GL(r,D) for a positive integer r and division F-algebra D of reduced…

We prove a nonlocal, nonlinear commutator estimate concerning the transfer of derivatives onto testfunctions. For the fractional $p$-Laplace operator it implies that solutions to certain degenerate nonlocal equations are higher…

Let $n$ be a non-negative integer, $R$ a commutative Noetherian ring, $\mathfrak{a}$ an ideal of $R$, $M$ and $N$ two finitely generated $R$-modules, and $X$ an arbitrary $R$-module. In this paper, we study cofiniteness and finiteness of…