相关论文: Separable bimodules and approximation

For a nice-enough category $\mathcal{C}$, we construct both the morphism category ${\rm H}(\mathcal{C})$ of $\mathcal{C}$ and the category ${\rm mod}\mbox{-}\mathcal{C}$ of all finitely presented contravariant additive functors over…

We give some basics about homological algebra of difference representations. We consider both the difference-discrete and the difference-rational case. We define the corresponding cohomology theories and show the existence of spectral…

Based upon properties of ordinal length, we introduce a new class of modules, the binary modules, and study their endomorphism ring. The nilpotent endomorphisms form a two-sided ideal, and after factoring this out, we get a commutative…

We describe the structure of module categories of finite dimensional algebras over an algebraically closed field for which the cycles of nonzero nonisomorphisms between indecomposable finite dimensional modules are finite (do not belong to…

We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the…

After recalling the definition of codes as modules over skew polynomial rings, whose multiplication is defined by using an automorphism and a derivation, and some basic facts about them, in the first part of this paper we study some of…

This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…

In this paper, we study homological dimensions of algebras linked by recollements of derived module categories, and establish a series of new upper bounds and relationships among their finitistic or global dimensions. This is closely…

Silting modules are abundant. Indeed, they parametrise the definable torsion classes over a noetherian ring, and the hereditary torsion pairs of finite type over a commutative ring. Also the universal localisations of a hereditary ring, or…

In this paper we study local cohomology of finitely generated bigraded modules over a standard bigraded ring with respect to the irrelevant bigraded ideals and establish a duality theorem. Several applications are considered.

We associate bicomplexes with several integrable models in such a way that conserved currents are obtained by a simple iterative construction. Gauge transformations and dressings are discussed in this framework and several examples are…

Consider the polynomial ring in countably infinitely many variables over a field of characteristic zero, together with its natural action of the infinite general linear group G. We study the algebraic and homological properties of finitely…

For a finite dimensional algebra $A$, we prove that the bounded homotopy category of projective $A$-modules and the bounded derived category of $A$-modules are dual to each other via certain categories of locally-finite cohomological…

The irreducible components of varieties parametrizing the finite dimensional representations of a finite dimensional algebra $\Lambda$ are explored, with regard to both their geometry and the structure of the modules they encode. Provided…

Let $R$ be a commutative noetherian ring. The $n$-semidualizing modules of $R$ are generalizations of its semidualizing modules. We will prove some basic properties of $n$-semidualizing modules. Our main result and example shows that the…

Using linear functional-based duality of modules, we generalize the syndrome decoding algorithm of linear codes over finite fields to those over finite commutative rings. Moreover, If the ring is local the algorithm is simplified by…

Fix a manifold M, and let V be an infinite dimensional Lie algebra of vector fields on M. Assume that V contains a finite dimensional semisimple maximal subalgebra A, the projective or conformal subalgebra. A projective or conformal…

We show that bounded type implies finite type for a constructible subcategory of the module category of a finitely generated algebra over a field, which is a variant of the first Brauer-Thrall conjecture. A full subcategory is constructible…

In this note, we extend the quasi-projective dimension of finite (that is, finitely generated) modules to homologically finite complexes, and we investigate some of homological properties of this dimension.

We start with observing that the only connected finite dimensional algebras with finitely many isomorphism classes of indecomposable bimodules are the quotients of the path algebras of uniformly oriented $A_n$-quivers modulo the radical…