Related papers: Vector spaces over finite commutative rings
In this expository article, we discuss the relation between the Gaussian binomial and multinomial coefficients and ordinary binomial and multinomial coefficients from a combinatorial viewpoint, based on expositions by Butler, Knuth and…
We discuss different generalizations of the classical notion of the index of a singular point of a vector field to the case of vector fields or 1-forms on singular varieties, describe relations between them and formulae for their…
We review the following subjects: 1. Basic theory on algebraic curves and their moduli space, 2. Schottky uniformization theory of Riemann surfaces, and its extension called arithmetic uniformization theory, 3. Application to these theories…
Arcs and caps are fundamental structures in finite projective spaces. They can be generalised. Here, a survey is given of some important results on these objects, in particular on generalised ovals and generalised ovoids. The paper also…
We formulate and prove relative versions of several classical decompositions known in the theory of Chevalley groups over commutative rings. As an application we obtain upper estimates for the width of principal congruence subgroups in…
We construct and study universal spaces for birational invariants of algebraic varieties over algebraic closures of finite fields.
A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…
We consider the vector space of $n \times n$ matrices over $\mathbb C$, Fermi operators and operators constructed from these matrices and Fermi operators. The properties of these operators are studied with respect to the underlying…
In this paper we consider the complex vector spaces of holomorphic cross-sections of homogeneous holomorphic vector bundles over elliptic adjoint orbits, and provide a sufficient condition for the vector spaces to be finite dimensional in…
The book is devoted to investigation of arithmetic of the matrix rings over certain classes of commutative finitely generated principal ideals domains. We mainly concentrate on constructing of the matrix factorization theory. We reveal a…
The present work aims to exploit the interplay between the algebraic properties of rings and the graph-theoretic structures of their associated graphs. We introduce commutatively closed graphs and investigate properties of commutatively…
Following our joint work arXiv:1003.4578 with Robert Langlands, we make the first steps toward developing geometric methods for analyzing trace formulas in the case of the function field of a curve defined over a finite field. We also…
We analyze Weierstrass cycles and tautological rings in moduli space of smooth algebraic curves and in moduli spaces of integral algebraic curves with embedded disks with special attention to moduli spaces of curves having genus $\leq 6$.…
We discuss the question when a finite-dimensional diffeological vector space is, or turns out not to be, the coproduct of its subspaces in the category of diffeological vector spaces, after reviewing the same question in some other…
We classify fields having finitely many finite non-commutative (not necessarily central) division algebras over them. In the process, we introduce the notion of anti-closure of a field and also make comments on fields having a linear…
We provide a variant of Baer's theorem about isomorphism of endomorphism rings of vector spaces over division rings, where the full endomorphism rings are replaced by some subrings of finitary maps.
We study some topological spaces that can be considered as hyperspaces associated to noncommutative spaces. More precisely, for a NC compact space associated to a unital C*-algebra, we consider the set of closed projections of the second…
We study the restricted families of projections in vector spaces over finite fields. We show that there are families of random subspaces which admit a Marstrand-Mattila type projection theorem.
In this paper, we consider some structures of linear codes over the ring $\mathcal{R}_k=R[v_1,\dots,v_k],$ where $v_i^2=v_i$ forall $i=1,\dots,k),$ and $R$ is a finite commutative Frobenius ring.
We prove the classification of the real vector subspaces of a quaternionic vector space by using a covariant functor which, to any pair formed of a quaternionic vector space and a real subspace, associates a coherent sheaf over the sphere.