Related papers: Graded-irreducible modules are irreducible

In this paper, we give a complete classification of extensions of finite irreducible conformal modules over rank two Lie conformal algebras.

We classify irreducible finite-dimensional modules of a collection of real Lie superalgebras that includes the simple ones, their classical variants, complex Lie superalgebras after restriction of scalars, and all real Lie algebras. Our…

We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…

Let $(R, \m)$ be a commutative Noetherian local ring with $\m^3 =(0)$. We give a condition for $R$ to have a non-free module of G-dimension zero. We shall also construct a family of non-isomorphic indecomposable modules of G-dimension zero…

The literature in persistent homology often refers to a "structure theorem for finitely generated graded modules over a graded principal ideal domain". We clarify the nature of this structure theorem in this context.

We characterize the canonical algebras such that for all dimension vectors of homogeneous modules the corresponding module varieties are complete intersections (respectively, normal). We also investigate the sets of common zeros of…

It is shown that a module is sequentially Cohen-Macaulay if and only if the index of reducibility for distinguished parameter ideals are eventually constant with special value. As corollaries to the main theorem we given to characterize the…

Let $G$ be a finite group and $H$ a normal subgroup of prime index $p$. Let $V$ be an irreducible ${\mathbb F}H$-module and $U$ a quotient of the induced ${\mathbb F}G$-module $V\kern-3pt\uparrow$. We describe the structure of $U$, which is…

We call a finite-dimensional K-algebra A geometrically irreducible if for all d all connected components of the affine scheme of d-dimensional A-modules are irreducible. We prove that a geometrically irreducible algebra with exactly two…

In this paper, we first classify all irreducible modules of the vertex algebra $V_L^+$ when $L$ is a negative definite even lattice of arbitrary rank. In particular, we show that any irreducible $V_L^+$-module is isomorphic to a submodule…

We give degree lower bounds for quotient line bundles of the lowest piece of a Hodge module induced by a complex variation of Hodge structures outside a simple normal crossing divisor, beyond the unipotent variation case. This note aims to…

We study the representations of a class of non-commutative polynomial algebras truncated at degree 3, with one additional relation. We determine the irreducible components of their varieties of representations. We do this by showing that…

Injective modules play an important role in characterizing different classes of rings (e.g. Noetherian rings, semisimple rings). Some semirings have no non-zero injective semimodules (e.g. the semiring of non-negative integers). In this…

In this article we study the combinatorics of congruence subgroups of the modular group. We consider the notion of minimal monomial solutions. These are the solutions of a matrix equation (also appearing in the study of Coxeter friezes),…

Let $G$ be an abelian group with identity $e$. Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper we will obtain some results concerning the graded generalized 2-absorbing submodules and their homogeneous…

In this paper we study graded Bourbaki ideals. It is a well-known fact that for torsionfree modules over Noetherian normal domains, Bourbaki sequences exist. We give criteria in terms of certain attached matrices for a homomorphism of…

We prove that the integral closedness of any ideal of height at least two is compatible with specialization by a generic element. This opens the possibility for proofs using induction on the height of an ideal. Also, with additional…

We study the classification of submodules of module categories over monoidal categories, extending ideas of Coulembier on the classification of tensor ideals in monoidal categories. We develop a framework that applies to module categories…

We give an explicit description of the irreducible components of the moduli spaces of polarized Enriques surfaces in terms of decompositions of the polarization as an effective sum of isotropic classes. We prove that infinitely many of…

Let $G$ be a group with identity $e$, $R$ be a commutative $G$-graded ring with unity $1$ and $M$ be a $G$-graded unital $R$-module. In this article, we introduce the concept of graded $1$-absorbing prime submodule. A proper graded…