Displaying similar documents to “A pure arithmetical definition of the class group”

Atomicity and the fixed divisor in certain pullback constructions

Jason Greene Boynton (2012)

Colloquium Mathematicae

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Let D be an integral domain with field of fractions K. In this article, we use a certain pullback construction in the spirit of Int(E,D) that furnishes many examples of domains between D[x] and K[x] in which there are elements that do not admit a finite factorization into irreducible elements. We also define the notion of a fixed divisor for this pullback construction to characterize all of its irreducible elements and those nonzero nonunits that do admit a finite factorization into...

On the asymptotic behavior of some counting functions

Maciej Radziejewski, Wolfgang A. Schmid (2005)

Colloquium Mathematicae

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The investigation of certain counting functions of elements with given factorization properties in the ring of integers of an algebraic number field gives rise to combinatorial problems in the class group. In this paper a constant arising from the investigation of the number of algebraic integers with factorizations of at most k different lengths is investigated. It is shown that this constant is positive if k is greater than 1 and that it is also positive if k equals 1 and the class...

On the factorization of reducible properties of graphs into irreducible factors

P. Mihók, R. Vasky (1995)

Discussiones Mathematicae Graph Theory

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A hereditary property R of graphs is said to be reducible if there exist hereditary properties P₁,P₂ such that G ∈ R if and only if the set of vertices of G can be partitioned into V(G) = V₁∪V₂ so that ⟨V₁⟩ ∈ P₁ and ⟨V₂⟩ ∈ P₂. The problem of the factorization of reducible properties into irreducible factors is investigated.