The tame degree and related invariants of non-unique factorizations

Franz Halter-Koch

Displaying similar documents to “The tame degree and related invariants of non-unique factorizations”

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.

A structure theorem for sets of lengths

Alfred Geroldinger (1998)

Colloquium Mathematicae

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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.

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...

Arithmetic of non-principal orders in algebraic number fields

Andreas Philipp (2010)

Actes des rencontres du CIRM

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Let $R$ be an order in an algebraic number field. If $R$ is a principal order, then many explicit results on its arithmetic are available. Among others, $R$ is half-factorial if and only if the class group of $R$ has at most two elements. Much less is known for non-principal orders. Using a new semigroup theoretical approach, we study half-factoriality and further arithmetical properties for non-principal orders in algebraic number fields.