Related papers: Linear groups over a locally linear division ring

A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…

In this paper we establish decomposition theorems for derivations of group rings. We provide a topological technique for studying derivations of a group ring $A[G]$ in case $G$ has finite conjugacy classes. As a result, we describe all…

In this paper, we study the genera of zero-divisor graphs with respect to ideals in finite rings.

We develop general foundations of topological algebra over a linearly topologized ring k in a format applicable to both formal schemes and analytic adic spaces. We are especially interested in determining exact closed tensor categories of…

We find explicit subdivision rules for all special cubulated groups. A subdivision rule for a group produces a sequence of tilings on a sphere which encode all quasi-isometric information for a group. We show how these tilings detect…

We prove that any finitely generated one ended group has linear end depth. Moreover, we give alternative proofs to theorems relating the growth of a finitely generated group to the number of its ends.

We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…

In this article we generalize a classical result by Passman on primeness of unital strongly group graded rings to the class of nearly epsilon-strongly group graded rings which are not necessarily unital. Using this result, we obtain (i) a…

We characterize the fundamental group of a locally finite graph G with ends combinatorially, as a group of infinite words. Our characterization gives rise to a canonical embedding of this group in the inverse limit of the (free) fundamental…

A survey of recent results about profinite groups, and results about infinite and finite groups where the theory of profinite groups plays a leading role.

We compute the equivariant fundamental class of the orbit closure of a linear series on the projective line. We also describe the boundary of the orbit closure and how the orbits specialise in one parameter families.

We introduce an approach to the categorification of rings, via the notion of distributive categories with negative objects, and use it to lay down categorical foundations for the study of super, quantum and non-commutative combinatorics.…

We study endomorphism rings of principally polarized abelian surfaces over finite fields from a computational viewpoint with a focus on exhaustiveness. In particular, we address the cases of non-ordinary and non-simple varieties. For each…

Pursuing a generalization of group symmetries of modular categories to category symmetries in topological phases of matter, we study linear Hopf monads. The main goal is a generalization of extension and gauging group symmetries to category…

In this paper, we study properties of polynomials over division rings. Moreover, we present formulas for finding roots of some polynomials

Groups of almost upper triangular infinite matrices with entries indexed by integers are studied. It is shown that, when the matrices are over a finite field, these groups admit a nondiscrete totally disconnected, locally compact group…

The goal of this paper is to provide some basic structure information on derivations in finite semirings.

The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…

Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…

The present survey aims at being a list of Conjectures and Problems in an area of model-theoretic algebra wide open for research, not a list of known results. To keep the text compact, it focuses on structures of finite Morley rank,…