On invariants related to non-unique factorizations in block monoids and rings of algebraic integers

Wolfgang Alexander Schmid

Displaying similar documents to “On invariants related to non-unique factorizations in block monoids and rings of algebraic integers”

Arithmetic of block monoids

Wolfgang Alexander Schmid (2004)

Mathematica Slovaca

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

Wolfgang A. Schmid (2005)

Journal de Théorie des Nombres de Bordeaux

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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. ...

A structure theorem for sets of lengths

Alfred Geroldinger (1998)

Colloquium Mathematicae

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Towards a more precise understanding of sets of lengths

Wolfgang A. Schmid (2010)

Actes des rencontres du CIRM

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This short survey, based on the content of a talk with the same title, summarizes some classical and recent results on the set of differences of an abelian group. We put a certain emphasize on ongoing joint work of A. Plagne and the author. We also briefly review the relevance of this notion in Non-unique Factorization Theory, in particular towards the subject mentioned in the title.

Zero-sumfree sequences in cyclic groups and some arithmetical application

Alfred Geroldinger, Yahya Ould Hamidoune (2002)

Journal de théorie des nombres de Bordeaux

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We show that in a cyclic group with $n$ elements every zero-sumfree sequence $S$ with length $| S | \geq \frac{n + 1}{2}$ contains some element of order $n$ with high multiplicity.

On delta sets and their realizable subsets in Krull monoids with cyclic class groups

Scott T. Chapman, Felix Gotti, Roberto Pelayo (2014)

Colloquium Mathematicae

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Let M be a commutative cancellative monoid. The set Δ(M), which consists of all positive integers which are distances between consecutive factorization lengths of elements in M, is a widely studied object in the theory of nonunique factorizations. If M is a Krull monoid with cyclic class group of order n ≥ 3, then it is well-known that Δ(M) ⊆ {1,..., n-2}. Moreover, equality holds for this containment when each class contains a prime divisor from M. In this note, we consider the question...