Czechoslovak Mathematical Journal, first online, pp. 1-10
Ideal class (semi)groups and atomicity in Prüfer domains
Richard Erwin Hasenauer
Received April 2, 2020. Published online December 10, 2020.
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.