Local tameness of v-noetherian monoids

By Alfred Geroldinger, W. Hassler. 2008

68 citations recorded by the source corpus.

Abstract Let H be a v -noetherian monoid, e.g., the multiplicative monoid R ∖ { 0 } of a noetherian domain R . We show that, for every b ∈ H , there exists a constant ω ( H , b ) ∈ N 0 having the following property: If n ∈ N and a 1 , … , a n ∈ H such that b divides the product a 1 ⋅ … ⋅ a n , then b already divides a subproduct of a 1 ⋅ … ⋅ a n consisting of at most ω ( H , b ) factors. Using the ω ( H , ⋅ ) -quantities we derive a new characterization of local tameness–a crucial finiteness property in the theory of non-unique factorizations.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/b7b7a78d5bdd93b34d2a5935e3b402f38b96d26e

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In Algebra and Number Theory

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Citations in the corpus

Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules (2016, background): “In the next proposition we collect some elementary properties of the above invariants that are well-known for cancellative monoids ([24, 25]).”
On the arithmetic of tame monoids with applications to Krull monoids and Mori domains (2010, background): “The ω(H, ·)-invariants have been studied in factorization theory for many years, but only recently was it shown that in a v-noetherian monoid we have ω(H, a) <∞ for all a ∈ H (see [24]).”
Factorization invariants of Puiseux monoids generated by geometric sequences (2019, methodology): “The omega function was introduced by Geroldinger and Hassler in [21] to measure how far in an atomic monoid an element is from being prime.”