Related papers: Radical-injectivy in the category S-Act

The injective spectrum is a topological space associated to a ring $R$, which agrees with the Zariski spectrum when $R$ is commutative noetherian. We consider injective spectra of right noetherian rings (and locally noetherian Grothendieck…

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…

The R-matrix formalism for the construction of integrable systems with infinitely many degrees of freedom is reviewed. Its application to Poisson, noncommutative and loop algebras as well as central extension procedure are presented. The…

We show that, for a principal ideal domain R, the homotopy category of Bousfield R-local spaces injects fully faithful into a homotopy category of simplicial pointed flat coalgebras.

Rational B\'{e}zier functions are widely used as mapping functions in surface reparameterization, finite element analysis, image warping and morphing. The injectivity (one-to-one property) of a mapping function is typically necessary for…

It is proved that a module M over a commutative noetherian ring R is injective if Ext^i((R/p)_p,M)=0 holds for every i\ge 1 and every prime ideal p in R. This leads to the following characterization of injective modules: If F is faithfully…

We study prime ideals, prime modules, and associated primes of graded modules over rings $S$ graded by a unique product monoid. We consider two situations in detail: (a) the case where $S$ is strongly group-graded and (b) the case where $S$…

A ring $R$ is called a J-regular ring if R/J(R) is von Neumann regular, where J(R) is the Jacobson radical of R. It is proved that if R is J-regular, then (i) R is right n-injective if and only if every homomorphism from an $n$-generated…

Given a small abelian category $\mathcal{A}$, the Freyd-Mitchell embedding theorem states the existence of a ring $R$ and an exact full embedding $\mathcal{A} \rightarrow R$-Mod. This theorem is useful as it allows one to prove general…

We present novel microlocal and injectivity analyses of ellipsoid and hyperboloid Radon transforms. We introduce a new Radon transform, $R$, which defines the integrals of a compactly supported $L^2$ function, $f$, over ellipsoids and…

Injective metric spaces, or absolute 1-Lipschitz retracts, share a number of properties with CAT(0) spaces. In the 1960es, J. R. Isbell showed that every metric space X has an injective hull E(X). Here it is proved that if X is the vertex…

By the Telescope Conjecture for Module Categories, we mean the following claim: "Let R be any ring and (A, B) be a hereditary cotorsion pair in Mod-R with A and B closed under direct limits. Then (A, B) is of finite type." We prove a…

An action of a compact Lie group is called equivariantly formal, if the Leray--Serre spectral sequence of its Borel fibration degenerates at the E_2-term. This term is as prominent as it is restrictive. In this article, also motivated by…

E. Bunch, P. Lofgren, A. Rapp and D. N. Yetter [J. Knot theory Ramifications (2010)] pointed out that by considering inner automorphism groups of quandles, one have a functor from the category of quandles with surjective homomorphisms to…

Let $R$ be a commutative ring with identity and let $V$ be a free $R$-module of rank $n$ for some $n\in\mathbb{N}$. Fixing an $R$-basis $\mathcal{E}$ of $V$, the symmetric group $\mathfrak{S}_n$ acts on $V$ by permuting $\mathcal{E}$ and…

This thesis concerns the dynamics and integrability of the Rajeev-Ranken (RR) model, a mechanical system with 3 degrees of freedom describing screw-type nonlinear wave solutions of a scalar field theory dual to the 1+1D SU(2) Principal…

Recently, in a series of papers "simple" versions of direct-injective and direct-projective modules have been investigated. These modules are termed as "simple-direct-injective" and "simple-direct-projective", respectively. In this paper,…

The aim of this paper is to study the notions of $\mathcal{A}$-C3 and $\mathcal{A}$-D3 modules for some class $\mathcal{A}$ of right modules. Several characterizations of these modules are provided and used to describe some well-known…

The main aim of this article is to study the relation between $F$-injective singularity and the Frobenius closure of parameter ideals in Noetherian rings of positive characteristic. The paper consists of the following themes, including many…

A ring $R$ is called right $\aleph_{0}$-injective if every homomorphism from a countably generated right ideal of $R$ to $R_{R}$ can be extended to a homomorphism from $R_{R}$ to $R_{R}$. In this note, some characterizations of…