Arithmetic of seminormal weakly Krull monoids and domains

By Alfred Geroldinger, Florian Kainrath, Andreas Reinhart. 2015

46 citations recorded by the source corpus.

We study the arithmetic of seminormal $v$-noetherian weakly Krull monoids with nontrivial conductor which have finite class group and prime divisors in all classes. These monoids include seminormal orders in holomorphy rings in global fields. The crucial property of seminormality allows us to give precise arithmetical results analogous to the well-known results for Krull monoids having finite class group and prime divisors in each class. This allows us to show, for example, that unions of sets of lengths are intervals and to provide a characterization of half-factoriality.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/def8a1a045dfda82219323f07d37fb10b30b1761

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In Algebra and Number Theory

1. S. Tringali
2. Alfred Geroldinger
3. Florian Kainrath
4. Yushuang Fan
5. Felix Gotti

In Geometry and Topology

1. Alfred Geroldinger
2. S. Tringali
3. Yushuang Fan

Citations in the corpus

• Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules (2016, background): “from numerical monoids to Mori domains, including semigroups of modules and maximal orders in central simple algebras (see, for example, [2, 4, 39, 26]).”