A structure theorem for sets of lengths

Alfred Geroldinger

Displaying similar documents to “A structure theorem for sets of lengths”

Arithmetic of block monoids

Wolfgang Alexander Schmid (2004)

Mathematica Slovaca

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Elasticity of factorizations in atomic monoids and integral domains

Franz Halter-Koch (1995)

Journal de théorie des nombres de Bordeaux

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For an atomic domain $R$ , its elasticity $ρ (R)$ is defined by : $ρ (R) = sup {m / n |u_{1} \dots u_{m} = v_{1} \dots v_{n}$ for irreducible $u_{j}, v_{i} \in R}$ . We study the elasticity of one-dimensional noetherian domains by means of the more subtle invariants $μ_{m} (R)$ defined by : $μ_{m} (R) = sup {n |u_{1} \dots u_{m} = u_{1} \dots v_{n}$ for irreducible $u_{j}, v_{i} \in R}$ . As a main result we characterize all orders in algebraic number fields having finite elasticity. On the way, we obtain a series of results concerning the invariants $μ_{m}$ and $ρ$ for monoids and integral domains which are of independent interest.

Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids

Víctor Blanco, Pedro A. García-Sánchez, Alfred Geroldinger (2010)

Actes des rencontres du CIRM

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Arithmetical invariants—such as sets of lengths, catenary and tame degrees—describe the non-uniqueness of factorizations in atomic monoids.We study these arithmetical invariants by the monoid of relations and by presentations of the involved monoids. The abstract results will be applied to numerical monoids and to Krull monoids.

Arithmetical theory of monoid homomorphisms.

A. Geroldinger, F. Halter-Koch (1994)

Semigroup forum

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Diversity in inside factorial monoids

Ulrich Krause, Jack Maney, Vadim Ponomarenko (2012)

Czechoslovak Mathematical Journal

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In a recent paper (Diversity in Monoids, Czech. Math. J. 62 (2012), 795–809), the last two authors introduced and developed the monoid invariant “diversity” and related properties “homogeneity” and “strong homogeneity”. We investigate these properties within the context of inside factorial monoids, in which the diversity of an element counts the number of its different almost primary components. Inside factorial monoids are characterized via diversity and strong homogeneity. A new invariant...

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...