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Displaying 441 – 460 of 1341

The fundamental constituents of iteration digraphs of finite commutative rings

Jizhu Nan, Yangjiang Wei, Gaohua Tang (2014)

Czechoslovak Mathematical Journal

For a finite commutative ring $R$ and a positive integer $k ⩾ 2$ , we construct an iteration digraph $G (R, k)$ whose vertex set is $R$ and for which there is a directed edge from $a \in R$ to $b \in R$ if $b = a^{k}$ . Let $R = R_{1} \oplus ... \oplus R_{s}$ , where $s > 1$ and $R_{i}$ is a finite commutative local ring for $i \in {1, ..., s}$ . Let $N$ be a subset of ${R_{1}, \dots, R_{s}}$ (it is possible that $N$ is the empty set $\emptyset$ ). We define the fundamental constituents $G_{N}^{*} (R, k)$ of $G (R, k)$ induced by the vertices which are of the form ${(a_{1}, \dots, a_{s}) \in R : a_{i} \in D (R_{i})$ if $R_{i} \in N$ , otherwise $a_{i} \in U (R_{i}), i = 1, ..., s},$ where U $(R)$ denotes the unit group of $R$ and D $(R)$ denotes the zero-divisor set of $R$ . We investigate...

The fundamental lemma of a relative trace formula for $G L (3)$

Yangbo Ye (1993)

Compositio Mathematica

The fundamental theorem of prehomogeneous vector spaces modulo $p^{m}$ (With an appendix by F. Sato)

Raf Cluckers, Adriaan Herremans (2007)

Bulletin de la Société Mathématique de France

For a number field $K$ with ring of integers $𝒪_{K}$ , we prove an analogue over finite rings of the form $𝒪_{K} / 𝒫^{m}$ of the fundamental theorem on the Fourier transform of a relative invariant of prehomogeneous vector spaces, where $𝒫$ is a big enough prime ideal of $𝒪_{K}$ and $m > 1$ . In the appendix, F.Sato gives an application of the Theorems 1.1, 1.3 and the Theorems A, B, C in J.Denef and A.Gyoja [Character sums associated to prehomogeneous vector spaces, Compos. Math., 113(1998), 237–346] to the functional equation of $L$ -functions...

Currently displaying 441 – 460 of 1341

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Displaying 441 – 460 of 1341

The fundamental constituents of iteration digraphs of finite commutative rings

The fundamental lemma of a relative trace formula for $G L (3)$

The fundamental theorem of prehomogeneous vector spaces modulo $p^{m}$ (With an appendix by F. Sato)

The $G L (n, F_{p})$ -invariance of the Potts Hamiltonian.

The Galois Cohomology of Pythagorean Fields.

The Galois Group of a Radical Extension of the Rationals.

The Galois group of the tangency problem for plane curves.

The Galois group of $X^{p} + a X^{s} + a$

The Galois module of a twisted element in the $p^{m}$ -th cyclotomic field

The Galois module structure of algebraic integer rings in fields with generalised quaternion group

The Galois structure of S-units

The Galois sturcture of the square root of the inverse different.

The Gaussian zoo.

The gcd-sum function.

The genera representing a positive integer

The general quasi-order algorithm in number theory.

The generalization and proof of Bertrand's postulate.

The Generalized Divisor Problem Over Arithmetic Progressions.

The generalized Hardy-Littlewood's problem involving a quadratic polynomial with coprime discriminants

The generalized Radon-Hurwitz numbers

Currently displaying 441 – 460 of 1341