Related papers: Computation of the classifying ring of formal modu…

We describe an algorithm for obtaining generators of the unit group of the integral group ring ZG of a finite abelian group G. We used our implementation in Magma of this algorithm to compute the unit groups of ZG for G of order up to 110.…

Several authors have introduced various type of coherent-like rings and proved analogous results on these rings. It appears that all these relative coherent rings and all the used techniques can be unified. In [2], several coherent-like…

We describe the computation of class groups and unit groups of number fields as implemented in Magma (V2.29). After quickly reviewing the main algorithms based on factor bases, relation collection, and analytic class number evaluation, we…

We introduce Backstr\"om pairs and Backstr\"om rings, study their derived categories and construct for them a sort of categorical resolutions. For the latter we define the global dimension, construct a sort of semi-orthogonal decomposition…

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…

We formulate generalizations of Pauli's theorem on the cases of real and complex Clifford algebras of even and odd dimensions. We give analogues of these theorems in matrix formalism. Using these theorems we present an algorithm for…

Let G be a simple algebraic group over an algebraically closed field of characteristic zero and X be a spherical conjugacy class of G. We determine the decomposition of the coordinate ring of X into simple G-modules.

We prove explicit and elementary formulas for the group homology and cohomology of a finite group with coefficients in any module. We describe in elementary terms the cohomology algebra $H^*(G,k)$ as a graded algebra for a finite group $G$…

In this note, we compute the split Grothendieck ring of a generalized category of Soergel bimodules of type $A_2$, where we take one generator for each reflection. We give a presentation by generators and relations of it and a…

The current paper is dedicated to the study of the classical $K_1$ groups of graded rings. Let $A$ be a $\Gamma$ graded ring with identity $1$, where the grading $\Gamma$ is an abelian group. We associate a category with suspension to the…

For a finite dimensional algebra $A$, we establish correspondences between torsion classes and wide subcategories in $mod(A)$. In case $A$ is representation finite, we obtain an explicit bijection between these two classes of subcategories.…

A twisted ring is a ring endowed with a family of endomorphisms satisfying certain relations. One may then consider the notions of twisted module and twisted differential module. We study them and show that, under some general hypothesis,…

Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…

Recall that an algebraic module is a KG-module that satisfies a polynomial with integer coefficients, with addition and multiplication given by direct sum and tensor product. In this article we prove that if L is a component of the (stable)…

For a complex simple Lie algebra of type A_l,B_l,C_l or D_l, given a family of elements f_\lambda\ in commutative ring Z[\Lambda], we show that f_\lambda\ is just the formal character of the Weyl module V(\lambda) if f_\lambda\ satisfy…

In Homotopy Type Theory, cohomology theories are studied synthetically using higher inductive types and univalence. This paper extends previous developments by providing the first fully mechanized definition of cohomology rings. These rings…

Let $\Lambda$ be a $\mathbb{Z}$-graded artin algebra. Two classical results of Gordon and Green state that if $\Lambda$ has only finitely many indecomposable gradable modules, up to isomorphism, then $\Lambda$ has finite representation…

The study of rings and modules with homological criteria is a cornerstone of commutative algebra. Let $R$ be a commutative Noetherian ring with identity (not necessarily local) and $\frak a$ a proper ideal of $R$. In this paper, a relative…

The main goal of the present paper is to generalize the results of~\cite{TroLNM,TroBoch} in the following way: To be able to define $K_0(A)\o\C$-valued Lefschetz numbers of the first type of an endomorphism $V$ on a C*-elliptic complex one…

In this paper, we compute the number of distinct centralizers of some classes of finite rings. We then characterize all finite rings with $n$ distinct centralizers for any positive integer $n \leq 5$. Further we give some connections…