Related papers: Injective modules over the Jacobson algebra $K< X,…

In this paper, we investigate the notions of $\mathcal{X}^\bot$-projective, $\mathcal{X}$-injective and $\mathcal{X}$-flat modules and give some characterizations of these modules, where $\mathcal{X}$ is a class of left $R$-modules. We…

Given a left noetherian k-algebra A graded by a group G, an injective object I in the category of G-graded A-modules and a morphism from G to another group G', we provide bounds for the injective dimension of I as a G'-graded A-module. For…

In this article an interpretation and a proof of some classical \\theorems in analysis on the integration of analytic vectors fields are derived from the algebraic method of realization of bialgebras which are constructed with the data of a…

A ring R is called right principally-injective if every R-homomorphism from a principal right ideal aR to R (a in R), extends to R, or equivalently if every system of equations xa=b (a, b in R) is solvable in R. In this paper we show that…

Following the structure theory approach for rings, the aim of this paper is to study some distinguished classes of Lie algebras. We introduce the notion of a Lie-module and discuss some relations of it with various classes of ideals of a…

In this paper we study injective modules over universal enveloping algebras of finite-dimensional Lie algebras over fields of arbitrary characteristic. Most of our results are dealing with fields of prime characteristic but we also…

Let $R$ be a regular domain containing a field $K$ of characteristic zero and let $D$ be the ring of $K$-linear differential operators on $R$. Let $E$ be an injective left $D$-module. We ask the question, when is $E$ injective as a…

This paper deals with sufficiency conditions for irreducibility of certain induced modules. We also construct irreducible representations for a group $G$ over a field ${\mathbb K}$ where the group $G$ is a semidirect product of a normal…

Let Q be a finite quiver without sources, and A be the corresponding algebra with radical square zero. We construct an explicit compact generator for the homotopy category of acyclic complexes of projective A-modules. We call such a…

Suppose we wish to embed an (associative) $k$-algebra $A$ in a $k$-algebra $R$ generated in some specified way; e.g., by two elements, or by copies of given $k$-algebras $A_1,$ $A_2,$ $A_3.$ Several authors have obtained sufficient…

Given two real algebraic varieties X and Y, we denote by R(X,Y) the set of all regular maps from X to Y. The set R(X,Y) is regarded as a topological subspace of the space C(X,Y) of all continuous maps from X to Y endowed with the…

We obtain a description of the C*-algebras which can occur as a simple quotient of the C*-algebra of a locally injective surjection on a compact metric space of finite covering dimension.

In this work we describe all simple modules over Leavitt path algebras as induced modules from irreducible representations of the isotropy groups.

In this paper, we first show that homogeneous Keller maps are injective on lines through the origin. We subsequently formulate a generalization, which is that under some conditions, a polynomial endomorphism with $r$ homogeneous parts of…

For any unital commutative ring $R$ and for any graph $E$, we identify the commutative core of the Leavitt path algebra of $E$ with coefficients in $R$, which is a maximal commutative subalgebra of the Leavitt path algebra. Furthermore, we…

We consider non-singular and Jacobian maps whose components are polynomial in the variable y. We prove that if a map has y-degree one, then it is the composition of a triangular map and a quasi-triangular map. We also prove that…

For a finite volume geodesic polyhedron P in hyperbolic 3-space, with the property that all interior angles between incident faces are integral submultiples of Pi, there is a naturally associated Coxeter group generated by reflections in…

In this paper we show that if $\Lambda=\amalg_{i\geq 0}\Lambda_i$ is a Koszul algebra with $\Lambda_0$ isomorphic to a product of copies of a field, then the minimal projective resolution of $\Lambda_0$ as a right $\Lambda$-module provides…

Let $K$ be a fixed field. We attach to each column-finite quiver $E$ a von Neumann regular $K$-algebra $Q(E)$ in a functorial way. The algebra $Q(E)$ is a universal localization of the usual path algebra $P(E)$ associated with $E$. The…

This survey of the recent developments in the investigations of a Leavitt path algebra L of an arbitrary graph E over a field K consists of two parts. In the first part describes how very often a single graph property of E implies multiple…