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Displaying similar documents to “Chains of factorizations in weakly Krull domains”

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 ∈ 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 ∈ [ 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 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 · . . . · u k for some irreducible elements u i , (ii) k ∈ L.

On relative integral bases for unramified extensions

Kevin Hutchinson (1995)

Acta Arithmetica

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0. Introduction. Since ℤ is a principal ideal domain, every finitely generated torsion-free ℤ-module has a finite ℤ-basis; in particular, any fractional ideal in a number field has an "integral basis". However, if K is an arbitrary number field the ring of integers, A, of K is a Dedekind domain but not necessarily a principal ideal domain. If L/K is a finite extension of number fields, then the fractional ideals of L are finitely generated and torsion-free (or, equivalently, finitely...