相关论文: Arithmetic of Units in F_q[T]

We investigate weight modules for finite and infinite Weyl algebras, classifying all such simple modules. We also study the representation type of the blocks of locally-finite weight module categories and describe indecomposable modules in…

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…

Describing the conjugacy classes of the unipotent upper triangular groups $\mathrm{UT}_{n}(\mathbb{F}_{q})$ uniformly (for all or many values of $n$ and $q$) is a nearly impossible task. This paper takes on the related problem of describing…

We are studying the fundamental tools for a quantum calculus based on the Tsallis $q$-exponential In particular we are looking at $q$-Fock spaces, structural identities, as well as rational functions in this context.

The aim of this paper is to obtain a uniform bound for a certain class of submodules from the following theorem: Let $(R,\frak m)$ be a local ring, let $M$ be a finite $R$--module of dimension $d\ge 1$ and let $\frak q$ be an ideal of $R$…

In this paper, the notion of F-schemes, a "generalization" of schemes, is introduced to cover unitary noncommutative rings.

In this note we present an algorithm for the construction of the unit group of the Burnside ring $\Omega(G)$ of a finite group $G$ from a list of representatives of the conjugacy classes of subgroups of G.

We study the behavior at infinity of ring $Q$-homeomorphisms with respect to $p$-modulus for $p>n$.

Let $\mathbb F$ denote an algebraically closed field, and fix a nonzero $q \in \mathbb F$ that is not a root of unity. We consider the $q$-tetrahedron algebra $\boxtimes_q$ over $\mathbb F$. It is known that each finite-dimensional…

We give a tableaux sum expression of $t$--analog of $q$--characters of finite dimensional representations (standard modules) of quantum affine algebras $\Ul$ when $\g$ is of type $A_n$, $D_n$.

During the past three decades fundamental progress has been made on constructing large torsion-free subgroups (i.e. subgroups of finite index) of the unit group $\U (\Z G)$ of the integral group ring $\Z G$ of a finite group $G$. These…

Properties of the $q$-ultraspherical polynomials for $q$ being a primitive root of unity are derived using a formalism of the $so_q(3)$ algebra. The orthogonality condition for these polynomials provides a new class of trigonometric…

We discuss arithmetic questions related to the "poor man's ad\`ele ring" $\mathcal A$ whose elements are encoded by sequences $(t_p)_p$ indexed by prime numbers, with each $t_p$ viewed as a residue in $\mathbb Z/p\mathbb Z$. Our main…

In this article the quantized matrix algebras as in the title have been studied at a root of unity. A full classification of simple modules over such quantized matrix algebras of rank $2$ along with a class of finite dimensional…

A noncommutative algebra of the complex $q$-twistors and their differentials is considered on the basis of the quantum $GL_q (4)\times SL_q (2)$ group. Real and pseudoreal $q$-twistors are discussed too. We consider the quantum-group…

Let F be the cyclotomic field of fifth roots of unity. We computationally investigate modularity of elliptic curves over F.

We determine the {\em real} counting function $N(q)$ ($q\in [1,\infty)$) for the hypothetical "curve" $C=\overline {\Sp \Z}$ over $\F_1$, whose corresponding zeta function is the complete Riemann zeta function. Then, we develop a theory of…

We show that the quotient of a Hom-finite triangulated category C by the kernel of the functor Hom(T, -), where T is a rigid object, is preabelian. We further show that the class of regular morphisms in the quotient admit a calculus of left…

Assuming everywhere good reduction we generalize the class number formula of Taelman to Drinfeld modules over arbitrary coefficient rings. In order to prove this formula we develop a theory of shtukas and their cohomology.

We investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers.