Results 41 to 50 of about 3,053 (239)

Generalized affine transformation monoids on Galois rings

International Journal of Mathematics and Mathematical Sciences, 2006
Let A be a ring with identity. The generalized affine transformation monoid Gaff(A) is defined as the set of all transformations on A of the form x↦xu+a (for all x∈A), where u,a∈A.
Yonglin Cao
doaj   +1 more source

Chebotarev's theorem for cyclic groups of order pq$pq$ and an uncertainty principle

Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3841-3856, December 2025.
Abstract Let p$p$ be a prime number and ζp$\zeta _p$ a primitive p$p$th root of unity. Chebotarev's theorem states that every square submatrix of the p×p$p \times p$ matrix (ζpij)i,j=0p−1$(\zeta _p^{ij})_{i,j=0}^{p-1}$ is nonsingular. In this paper, we prove the same for principal submatrices of (ζnij)i,j=0n−1$(\zeta _n^{ij})_{i,j=0}^{n-1}$, when n=pr ...
Maria Loukaki
wiley   +1 more source

A single source theorem for primitive points on curves

Forum of Mathematics, Sigma
Let C be a curve defined over a number field K and write g for the genus of C and J for the Jacobian of C. Let $n \ge 2$ . We say that an algebraic point $P \in C(\overline {K})$ has degree n if the extension $K(P)/K$ has degree n. By
Maleeha Khawaja, Samir Siksek
doaj   +1 more source

A note on the cohomology of moduli spaces of local shtukas

Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3709-3729, December 2025.
Abstract We study localized versions of spectral action of Fargues–Scholze, using methods from higher algebra. As our main motivation and application, we deduce a formula for the cohomology of moduli spaces of local shtukas under certain genericity assumptions, and discuss its relation with the Kottwitz conjecture.
David Hansen, Christian Johansson
wiley   +1 more source

On Azumaya algebras with a finite automorphism group

International Journal of Mathematics and Mathematical Sciences, 2001
Let B be a ring with 1, C the center of B, and G a finite automorphism group of B. It is shown that if B is an Azumaya algebra such that B=⊕∑g∈GJg where Jg={b∈B|bx=g(x)b   for all   x∈B}, then there exist orthogonal central idempotents {fi∈C|i=1,2,…,m ...
George Szeto, Lianyong Xue
doaj   +1 more source

Computing a Group of Polynomials over a Galois Field in FPGA Architecture

Mathematics, 2021
For the most extensive range of tasks, such as real-time data processing in intelligent transport systems, etc., advanced computer-based techniques are required. They include field-programmable gate arrays (FPGAs).
Sergei V. Shalagin
doaj   +1 more source

Symmetric Galois groups under specialization

Israel Journal of Mathematics, 2022
Given an irreducible bivariate polynomial $f(t,x)\in \mathbb{Q}[t,x]$, what groups $H$ appear as the Galois group of $f(t_0,x)$ for infinitely many $t_0\in \mathbb{Q}$? How often does a group $H$ as above appear as the Galois group of $f(t_0,x)$, $t_0\in \mathbb{Q}$?
Monderer, Tali, Neftin, Danny
openaire   +2 more sources

Iitaka fibrations and integral points: A family of arbitrarily polarized spherical threefolds

Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.
Abstract Studying Manin's program for a family of spherical log Fano threefolds, we determine the asymptotic number of integral points whose height associated with an arbitrary ample line bundle is bounded. This confirms a recent conjecture by Santens and sheds new light on the logarithmic analog of Iitaka fibrations, which have not yet been adequately 
Ulrich Derenthal, Florian Wilsch
wiley   +1 more source

On separable abelian extensions of rings

International Journal of Mathematics and Mathematical Sciences, 1982
Let R be a ring with 1, G(=〈ρ1〉×…×〈ρm〉) a finite abelian automorphism group of R of order n where 〈ρi〉 is cyclic of order ni. for some integers n, ni, and m, and C the center of R whose automorphism group induced by G is isomorphic with G.
George Szeto
doaj   +1 more source

The m$m$‐step solvable anabelian geometry of mixed‐characteristic local fields

Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.
Abstract Let K$K$ be a mixed‐characteristic local field. For an integer m⩾0$m \geqslant 0$, we denote by Km/K$K^m / K$ the maximal m$m$‐step solvable extension of K$K$, and by GKm$G_K^m$ the maximal m$m$‐step solvable quotient of the absolute Galois group GK$G_K$ of K$K$.
Seung‐Hyeon Hyeon
wiley   +1 more source