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A characterization of Krull monoids for which sets of lengths are (almost) arithmetical progressions

Geroldinger, Alfred ; Schmid, Wolfgang Alexander

Revista matemática iberoamericana, 2021-01, Vol.37 (1), p.293-316 [Periódico revisado por pares]

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Título:
A characterization of Krull monoids for which sets of lengths are (almost) arithmetical progressions
Autor: Geroldinger, Alfred ; Schmid, Wolfgang Alexander
Assuntos: Commutative Algebra ; Commutative rings and algebras ; Group theory and generalizations ; Mathematics ; Number Theory
É parte de: Revista matemática iberoamericana, 2021-01, Vol.37 (1), p.293-316
Descrição: Let $H$ be a Krull monoid with finite class group $G$ and suppose that every class contains a prime divisor. Then sets of lengths in $H$ have a well-defined structure which depends only on the class group $G$. With methods from additive combinatorics we establish a characterization of those class groups $G$ guaranteeing that all sets of lengths are (almost) arithmetical progressions.
Editor: Zuerich, Switzerland: European Mathematical Society Publishing House
Idioma: Inglês;Espanhol

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