Related papers: On the Image of the Totaling Functor

In this paper, by using functor rings and functor categories, we study finiteness and purity of subcategories of the module categories. We give a characterisation of contravariantly finite resolving subcategories of the module category of…

We develop the basic constructions of homological algebra in the (appropriately defined) unbounded derived categories of modules over algebras over coalgebras over noncommutative rings (which we call semialgebras over corings). We define…

Module is effective representation of ring in Abelian group. Linear map of module over commutative ring is morphism of corresponding representation. This definition is the main subject of the book. To consider this definition from more…

We study maximal almost rigid modules over a gentle algebra $A$. We prove that the number of indecomposable direct summands of every maximal almost rigid $A$-module is equal to the sum of the number of vertices and the number of arrows of…

We overview numerous algorithms in computational $D$-module theory together with the theoretical background as well as the implementation in the computer algebra system \textsc{Singular}. We discuss new approaches to the computation of…

In this paper, we define finitely additive, probability and modular functions over semiring-like structures. We investigate finitely additive functions with the help of complemented elements of a semiring. We also generalize some classical…

Let $D$ be an integrally closed domain with quotient field $K$. Let $A$ be a torsion-free $D$-algebra that is finitely generated as a $D$-module. For every $a$ in $A$ we consider its minimal polynomial $\mu_a(X)\in D[X]$, i.e. the monic…

We know that the model theory of modules leads to a way of obtaining definable categories of modules over a ring $R$ as the kernels of certain functors $(R\textbf{-Mod})^{\text{op}}\to\textbf{Ab}$ rather than of functors…

This paper develops a duality theory for connected cochain DG algebras, with particular emphasis on the non-commutative aspects. One of the main items is a dualizing DG module which induces a duality between the derived categories of DG…

Let $A$ be a commutative noetherian ring, let $\mathfrak{a}\subseteq A$ be an ideal, and let $I$ be an injective $A$-module. A basic result in the structure theory of injective modules states that the $A$-module $\Gamma_{\mathfrak{a}}(I)$…

Let $R$ be an associative ring with unit. This paper deals with various aspects of the category of functors of $\mathcal R$-modules; that is, the category of additive and covariant functors from the category of R-modules to the category of…

We count the number of submodules of an arbitrary module over a countable noetherian commutative ring. We give, along the way, a structural description of meager modules, which are defined as those that do not have the square of a simple…

This paper is primarily intended as an introduction for the mathematically inclined to some of the rich algebraic combinatorics arising in for instance CFT. It is essentially self-contained, apart from some of the background motivation and…

We introduce a generalization of the notion of a negligible morphism and study the associated tensor ideals and thick ideals. These ideals are defined by considering deformations of a given monoidal category $\mathcal{C}$ over a local ring…

We present basic properties of Gr\"obner bases of submodules of a free module of finite rank over a polynomial ring $R$ with coefficients in a graded truncated discrete valuations ring $A$. As an application, we give a criterion for a…

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…

A functor of sets $\mathbb X$ over the category of $K$-commutative algebras is said to be an affine functor if its functor of functions, $\mathbb A_{\mathbb X}$, is reflexive and $\mathbb X=\Spec \mathbb A_{\mathbb X}$. We prove that affine…

In this paper we study categories of tilting modules. Our starting point is the tilting modules for a reductive algebraic group G in positive characteristic. Here we extend the main result in [8] by proving that these tilting modules form a…

A commutative ring R has finite rank r, if each ideal of R is generated at most by r elements. A commutative ring R has the r-generator property, if each finitely generated ideal of R can be generated by r elements. Such rings are closely…

We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…