Displaying similar documents to “A “ v -operation free” approach to Prüfer v -multiplication domains.”

Ideal class (semi)groups and atomicity in Prüfer domains

Richard Erwin Hasenauer (2021)

Czechoslovak Mathematical Journal

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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.