Abstract
We explore the connection between atomicity in Prüfer domains and their corresponding class groups. We observe that a class group of infinite order is necessary for non-Noetherian almost Dedekind and Prüfer domains of finite character to be atomic. We construct a non-Noetherian almost Dedekind domain and exhibit a generating set for the ideal class semigroup.
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Hasenauer, R.E. Ideal class (semi)groups and atomicity in Prüfer domains. Czech Math J 71, 891–900 (2021). https://doi.org/10.21136/CMJ.2020.0136-20
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DOI: https://doi.org/10.21136/CMJ.2020.0136-20