Geodesic
Ideal class (semi)groups and atomicity in Prüfer domains
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 3, pp. 891-900

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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.
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.
DOI : 10.21136/CMJ.2020.0136-20
Classification : 13A50, 13F15
Keywords: Prüfer domain; factorization 
Hasenauer, Richard Erwin. Ideal class (semi)groups and atomicity in Prüfer domains. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 3, pp. 891-900. doi: 10.21136/CMJ.2020.0136-20
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     title = {Ideal class (semi)groups and atomicity in {Pr\"ufer} domains},
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     pages = {891--900},
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     mrnumber = {4295253},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0136-20/}
}
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