Related papers: Few remarks on essential modules

This paper is a contribution to the construction of non-semisimple modular categories. We establish when M\"uger centralizers inside non-semisimple modular categories are also modular. As a consequence, we obtain conditions under which…

We prove complete reducibility for an integrable module for an affine Lie algebra where the canonical central element acts non-trivially. We further prove that integrable modules does not exists for most of the super affine Lie algebras…

This work completes the classification of the imprimitive irreducible modules, over algebraically closed fields of characteristic 0, of the finite quasisimple groups.

Let $A\subset B$ be an integral ring extension of integral domains with fields of fractions $K$ and $L$, respectively. The integral degree of $A\subset B$, denoted by ${\rm d}_A(B)$, is defined as the supremum of the degrees of minimal…

Let $\mathfrak{a}$ be an ideal of a commutative noetherian ring $R$, $\mathcal{S}$ a Serre subcategory of $R$-modules satisfying the condition $C_\mathfrak{a}$ and $\mathcal{N}$ the subcategory of finitely generated $R$-modules. In this…

Let $(R,\mathfrak{m})$ be a commutative Noetherian local ring, $M$ be a finitely generated $R$-module and $\mathfrak{a}$, $I$ and $J$ be ideals of $R$. We investigate the structure of formal local cohomology modules of…

A module is called absolutely indecomposable if it is directly indecomposable in every generic extension of the universe. We want to show the existence of large abelian groups that are absolutely indecomposable. This will follow from a more…

A semidualizing module is a generalization of Grothendieck's dualizing module. For a local Cohen-Macaulay ring $R$, the ring itself and its canonical module are always realized as (trivial) semidualizing modules. Reasonably, one might…

We introduce an abstract notion of a 3D-rotation module for a group $G$ that does not require the module to carry a vector space structure, a priori nor a posteriori. We prove that, under an expected irreducibility-like assumption, the only…

Rao and Zhao classified the irreducible integrable modules with finite dimensional weight spaces for the untwisted affine superalgebras which are not $\hat{A}(m,n)$ ($m\ne n$) or $\hat{C}(m)$. Here we treat the latter affine superalgebras…

In this paper which is the first of a series of papers on smooth structures, the concepts of C-structures and smooth structures are introduced and studied. The notion of smooth structure on semi-integral domains is given. It is shown that…

In this paper, considering the difference between the finiteness dimension and cohomological dimension for a finitely generated module, we investigate the asymptotic behavior of grades of components of graded local cohomology modules with…

In the category of finitely generated modules over an artinian ring, we classify all the abelian exact subcategories closed under predecessors or, equivalently, all the split torsion pairs with torsion-free class closed under quotients.

Given a right R-module M and any short exact sequence of right R-modules \[ 0 \to A \to B \to C \to 0, \] it is well known that if both A and C belong to the subinjectivity domain $\mathfrak{\underline{In}^{-1}}(M)$ (resp., the…

We give necessary conditions on complete embedded \cmc surfaces with three or four ends subject to reflection symmetries. The respective submoduli spaces are two-dimensional varieties in the moduli spaces of general \cmc surfaces. We…

Let $(A,\mathfrak{m})$ be a short Artin local ring (i.e., $\mathfrak{m}^3 = 0$ and $\mathfrak{m}^2 \neq 0$). Assume $A$ is not a hypersurface ring. We show there exists $c_A \geq 2$ such that if $M$ is any finitely generated module with…

Torsion pairs in the category of finitely presented modules over a noetherian ring can be parametrised by the class of cosilting modules. In this paper, we characterise such modules in terms of their indecomposable summands, providing a new…

We describe the category of integrable sl(1|n)^ -modules with the positive central charge and show that the irreducible modules provide the full set of irreducible representations for the corresponding simple vertex algebra.

We prove that the group of automorphisms of the category of free modules over Noterian rings is semi-inner and present also a short proof of a similar result for the variery of Lie algebras.

In this paper, we introduce a topology on the set of isomorphism classes of finitely generated modules over an associative algebra. Then we focus on the relative topology on the set of isomorphism classes of maximal Cohen--Macaulay modules…