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Displaying 21 – 40 of 169

Arithmetical properties of finite rings and algebras, and analytic number theory. III. Finite modules and algebras over Dedekind domains.

John Knopfmacher (1973)

Journal für die reine und angewandte Mathematik

Birings and plethories of integer-valued polynomials

Jesse Elliott (2010)

Actes des rencontres du CIRM

Let $A$ and $B$ be commutative rings with identity. An $A$ - $B$ -biring is an $A$ -algebra $S$ together with a lift of the functor ${Hom}_{A} (S, -)$ from $A$ -algebras to sets to a functor from $A$ -algebras to $B$ -algebras. An $A$ -plethory is a monoid object in the monoidal category, equipped with the composition product, of $A$ - $A$ -birings. The polynomial ring $A [X]$ is an initial object in the category of such structures. The $D$ -algebra $Int (D)$ has such a structure if $D = A$ is a domain such that the natural $D$ -algebra homomorphism $θ_{n} : {⨂_{D}}_{i = 1}^{n} Int (D) \to Int (D^{n})$ is an isomorphism for...

Cale Bases in Algebraic Orders

Martine Picavet-L’Hermitte (2003)

Annales mathématiques Blaise Pascal

Let $R$ be a non-maximal order in a finite algebraic number field with integral closure $\bar{R}$ . Although $R$ is not a unique factorization domain, we obtain a positive integer $N$ and a family $𝒬$ (called a Cale basis) of primary irreducible elements of $R$ such that $x^{N}$ has a unique factorization into elements of $𝒬$ for each $x \in R$ coprime with the conductor of $R$ . Moreover, this property holds for each nonzero $x \in R$ when the natural map $Spec (\bar{R}) \to Spec (R)$ is bijective. This last condition is actually equivalent to several properties linked...

Chains of factorizations in weakly Krull domains

Alfred Geroldinger (1997)

Colloquium Mathematicae

Complete residue systems in the quadratic domain $ℤ (e^{2 π i / 3})$ .

Bergum, Gerald E. (1978)

International Journal of Mathematics and Mathematical Sciences

Concerning Filtrations on Commutative Rings.

John W. Petro (1975)

Manuscripta mathematica

Congruence monoids

Alfred Geroldinger, Franz Halter-Koch (2004)

Acta Arithmetica

Construction of $p o$ -groups with quasi-divisors theory

Jiří Močkoř (2000)

Czechoslovak Mathematical Journal

A method is presented making it possible to construct $p o$ -groups with a strong theory of quasi-divisors of finite character and with some prescribed properties as subgroups of restricted Hahn groups $H (Δ, ℤ)$ , where $Δ$ are finitely atomic root systems. Some examples of these constructions are presented.

Construction, sur un anneau de Dedekind, d'une base reguliere de polynomes a valeurs entieres.

Gilbert Gerboud (1989)

Manuscripta mathematica

Convexity, valuations and Prüfer extensions in real algebra.

Knebusch, Manfred, Zhang, Digen (2005)

Documenta Mathematica

Cycles of polynomial mappings in several variables over rings of integers in finite extensions of the rationals

T. Pezda (2003)

Acta Arithmetica

Décomposition du Galois-module des entiers d'une extension cyclique de degré premier d'un corps local ou d'un corps de nombres

Françoise Bertrandias (1975/1977)

Séminaire de théorie des nombres de Grenoble

Décomposition du Galois-module des entiers d'une extension cyclique de degré premier d'un corps de nombres ou d'un corps local

Françoise Bertrandias (1979)

Annales de l'institut Fourier

Soit $A$ un anneau de Dedekind, de corps des fractions $K$ , et soit $L$ une extension galoisienne de $K$ , dont le groupe de Galois $G$ est cyclique d’ordre premier. On note $B$ la clôture intégrale de $A$ dans $L$ . Il existe une unique décomposition du $A [G]$ -module $B$ en somme directe de sous-modules indécomposables. On détermine cette décomposition lorsque $K$ est un corps local ou un corps de nombres. Le résultat dépend d’une part des caractères irréductibles de $G$ sur $K$ , d’autre part des nombres de ramification associés...

Der allgemeine Approximationssatz für Manisbewertungen.

Joachim Gräter (1982)

Monatshefte für Mathematik

Determining Integer-Valued Polynomials From Their Image

Vadim Ponomarenko (2010)

Actes des rencontres du CIRM

This note summarizes a presentation made at the Third International Meeting on Integer Valued Polynomials and Problems in Commutative Algebra. All the work behind it is joint with Scott T. Chapman, and will appear in [2]. Let $Int (ℤ)$ represent the ring of polynomials with rational coefficients which are integer-valued at integers. We determine criteria for two such polynomials to have the same image set on $ℤ$ .

Differences in sets of lengths of Krull monoids with finite class group

Wolfgang A. Schmid (2005)

Journal de Théorie des Nombres de Bordeaux

Let $H$ be a Krull monoid with finite class group where every class contains some prime divisor. It is known that every set of lengths is an almost arithmetical multiprogression. We investigate which integers occur as differences of these progressions. In particular, we obtain upper bounds for the size of these differences. Then, we apply these results to show that, apart from one known exception, two elementary $p$ -groups have the same system of sets of lengths if and only if they are isomorphic.

Currently displaying 21 – 40 of 169