Elsevier

Journal of Algebra

Volume 444, 15 December 2015, Pages 201-245
Journal of Algebra

Arithmetic of seminormal weakly Krull monoids and domains

https://doi.org/10.1016/j.jalgebra.2015.07.026Get rights and content
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Abstract

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.

MSC

13A05
13F05
13F15
13F45
20M13

Keywords

Non-unique factorizations
Sets of lengths
Half-factoriality
Weakly Krull domains
Seminormal domains
Non-principal orders

Cited by (0)

This work was supported by the Austrian Science Fund FWF (Project Number P26036-N26).