Finite cyclic groups and the k-HFD property

Scott Chapman; William Smith

Displaying similar documents to “Finite cyclic groups and the k-HFD property”

Factorization in Krull monoids with infinite class group

Florian Kainrath (1999)

Colloquium Mathematicae

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Let H be a Krull monoid with infinite class group and such that each divisor class of H contains a prime divisor. We show that for each finite set L of integers ≥2 there exists some h ∈ H such that the following are equivalent: (i) h has a representation $h = u_{1} \cdot . . . \cdot u_{k}$ for some irreducible elements $u_{i}$ , (ii) k ∈ L.

On A Combinatorial Problem Connected withFactorizations

Weidong Gao (1997)

Colloquium Mathematicae

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Chains of factorizations in weakly Krull domains

Alfred Geroldinger (1997)

Colloquium Mathematicae

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Chains of factorizations in orders of global fields

Alfred Geroldinger (1997)

Colloquium Mathematicae

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A generalization of Davenport's constant and its arithmetical applications

Franz Halter-Koch (1992)

Colloquium Mathematicae

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On zero-testing and interpolation of sums of characters.

Dress, Andreas, Grabmeier, Johannes (1989)

Séminaire Lotharingien de Combinatoire [electronic only]

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Characters of finite groups and divisibility problems. (Charaktere endlicher Gruppen und Teilbarkeitsfragen.)

Kerber, Adalbert (1981)

Séminaire Lotharingien de Combinatoire [electronic only]

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The catenary degree of Krull monoids I

Alfred Geroldinger, David J. Grynkiewicz, Wolfgang A. Schmid (2011)

Journal de Théorie des Nombres de Bordeaux

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Let $H$ be a Krull monoid with finite class group $G$ such that every class contains a prime divisor (for example, a ring of integers in an algebraic number field or a holomorphy ring in an algebraic function field). The catenary degree $c (H)$ of $H$ is the smallest integer $N$ with the following property: for each $a \in H$ and each two factorizations $z, z^{'}$ of $a$ , there exist factorizations $z = z_{0}, ..., z_{k} = z^{'}$ of $a$ such that, for each $i \in [1, k]$ , $z_{i}$ arises from $z_{i - 1}$ by replacing at most $N$ atoms from $z_{i - 1}$ by at most $N$ new atoms. Under a very...

Factorization problems in class number two

Franz Halter-Koch (1993)

Colloquium Mathematicae

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The growth of regular functions on algebraic sets

A. Strzeboński (1991)

Annales Polonici Mathematici

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We are concerned with the set of all growth exponents of regular functions on an algebraic subset V of $ℂ^{n}$ . We show that its elements form an increasing sequence of rational numbers and we study the dependence of its structure on the geometric properties of V.