Related papers: Additive unit representations in global fields - A…

The theory of Gromov-Hausdorff convergence is applied to sequences of quotient rings of integers. It is shown the existence of limit rings (fields) as the Gromov-Hausdorff limits of sequences of metric quotient rings. The relation of these…

Previous research on exceptional units has primarily focused on the ring of rational integers or abstract finite rings, often restricted to linear or quadratic constraints. In this paper, we extend the concept of polynomial-type exceptional…

We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.

In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…

Given a collection $\{ G_i\}_{i=1}^d$ of finite groups and a ring $R$, we have previously introduced and studied certain foundational properties of the join ring $\mathcal{J}_{G_1, G_2, \ldots, G_d}(R)$. This ring bridges two extreme…

These notes collect results about algebraic correspondences and adapt them to the setting of correspondences on projective lines. The focus lies on finite orbits of algebraic correspondences. The main result is a field theoretic…

We analyze the abstract representations of the groups of rational points of even-dimensional quasi-split special unitary groups associated with quadratic field extensions. We show that, under certain assumptions, such representations have a…

We initiate a study of the rings of invariants of modular representations of elementary abelian p-groups. With a few notable exceptions, the modular representation theory of an elementary abelian p-group is wild. However, for a given…

We describe derivations of several important associative and Lie rings of infinite matrices over general rings of coefficients.

This paper focuses on greedy expansions, one possible representation of numbers, and on arithmetical operations with them. Performing addition or multiplication some additional digits can appear. We study bounds on the number of such digits…

An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…

Let $R$ be a local ring of characteristic $p>0$ which is $F$-finite and has perfect residue field. We compute the generalized Hilbert-Kunz invariant for certain modules over several classes of rings: hypersurfaces of finite representation…

We study clean group rings and also the group rings whose every element is a sum of two units. We also prove that if R is an Abelian exchange ring and G is a locally finite group, then the group ring RG has stable range one.

This is a survey article for "Handbook of Linear Algebra", 2nd ed., Chapman & Hall/CRC, 2014. An informal introduction to representations of quivers and finite dimensional algebras from a linear algebraist's point of view is given. The…

In this paper, we study arbitrary models of the first-order theory of a ring $A$ where the additive group $A$ is a finitely generated abelian group. Following an earlier paper by this author, Alexei G. Myasnikov and Francis Oger, we call…

Generators and relations are given for the subalgebra of cocommutative elements in the quantized coordinate rings of the classical groups, where the deformation parameter q is transcendental. This is a ring theoretic formulation of the well…

In this text, we are concerned with ring epimorphisms, and more specifically universal localisations, from path algebras to matrix algebras. We are mainly focused on constructing ring epimorphisms and universal localisations by extending…

In this paper, we develop an explicit method to express finite algebraic numbers (in particular, certain idempotents among them) in terms of linear recurrent sequences, and give applications to the characterization of the splitting primes…

In this article it is determined which integral reflection representations of the symmetric groups and the primitive complex reflection groups of degree $2$ have rings of invariants which are isomorphic to polynomial rings.

We give a survey of recent developments in the investigation of the various local-global conjectures for representations of finite groups.