Related papers: Ulrich modules and weakly lim Ulrich sequences do …

In this paper, given a simple linear recurrence sequence of algebraic numbers, which has either a dominant characteristic root or exactly two characteristic roots of maximal modulus, we give some explicit lower bounds for the index beyond…

This paper studies Ulrich ideals in one-dimensional Cohen-Macaulay local rings. A correspondence between Ulrich ideals and overrings is given. Using the correspondence, chains of Ulrich ideals are closely explored. The specific cases where…

This paper studies the existence of Auslander-Reiten sequences in subcategories of mod A, where A is a finite dimensional algebra over a field. The two main theorems give necessary and sufficient conditions for the existence of…

In this paper, we give a relation between the Hilbert multiplicity and the irreducible multiplicity. As an application, we characterize Ulrich modules in term of the irreducible multiplicity.

This paper investigates Ulrich bundles on decomposable threefold scrolls X over the Hirzebruch surface $\mathbb F_a$, for any integer $a \geq 0$, focusing on the study of their structure and classification. We prove existence of such Ulrich…

In this paper, we introduce a new concept in Nil-semicommutative modules and present it as an extension of Nil-semicommutative rings to modules. We prove that the class of Nil-semicommutative modules is contained in the class of Weakly…

We study moduli spaces of vector bundles on a two-dimensional neighbourhood $Z_k$ of an irreducible curve $\ell = CP^1$ with $\ell^2 = -k$ and give an explicit construction of these moduli as stratified spaces. We give sharp bounds for the…

Recently, Meierfrankenfeld has published three theorems on the cohomology of a finitary module. They cover the local determination of complete reducibility; the local splitting of group extensions; and the representation of locally split…

We characterize the existence of an Ulrich vector bundle on a variety $X \subset P^N$ in terms of the existence of a subvariety satisfying some precise conditions. Then we use this fact to prove that a complete intersection of dimension $n…

Let $R$ be a commutative Noetherian ring, $\Phi$ a system of ideals of $R$ and $I\in \Phi$. Let $M$ be an $R$-module (not necessary $I$-torsion) such that $\dim M\leq 1$, then the $R$-module $\Ext^i_{R}(R/I, M)$ is weakly Laskerian, for all…

We consider the 2-D incompressible Euler equations in a bounded domain and show that local weak solutions are exponentially integrable, uniformly in time, under minimal integrability conditions. This is a Serrin-type interior regularity…

A partition of the set of unary pp formulas into four regions is presented, which has a bearing on various structural properties of modules. The machinery developed allows for applications to IF, weakly coherent, nonsingular, and reduced…

This article proves the existence and regularity of weak solutions for a class of mixed local-nonlocal problems with singular nonlinearities. We examine both the purely singular problem and perturbed singular problems. A central…

An associative ring with 1 is said to be semilocal provided it is semisimple artinian modulo its Jacobson radical, that is, modulo its Jacobson radical it is isomorphic to a finite product of matrices over division rings. Modules with a…

Let R be a commutative ring with identity and M be an R-module. In this paper, we will introduce the concept of 2-irreducible (resp., strongly 2- irreducible) submodules of M as a generalization of irreducible (resp., strongly irreducible)…

In this note, some properties of finitely generated two-periodic modules over commutative Noetherian local rings have been studied. We show that under certain assumptions on a pair of modules $\left(M,N \right)$ with $M$ two-periodic, the…

We prove that if the local second-order structure function exponents in the inertial range remain positive uniformly in viscosity, then any spacetime $L^2$ weak limit of Leray--Hopf weak solutions of the Navier-Stokes equations on any…

This article concerns linear parts of minimal resolutions of finitely generated modules over commutative local, or graded rings. The focus is on the linearity defect of a module, which marks the point after which the linear part of its…

In this study, all rings are commutative with non-zero identity and all modules are considered to be unital. Let $M$ be a left $R$-module. A proper submodule $N$ of $M$ is called an $S$-$weakly$ $prime$ submodule if $0_{M}\neq f(m)\in N$…

Let R be a commutative noetherian local ring. As an analogue of the notion of the dimension of a triangulated category defined by Rouquier, the notion of the dimension of a subcategory of finitely generated R-modules is introduced in this…