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.
Keywords:  Prüfer domain; factorization
Classification MSC:  13A50, 13F15
DOI:  10.21136/CMJ.2020.0136-20

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Affiliations:   Richard Erwin Hasenauer, Northeastern State University, 600 N Grand Ave, Tahlequah, OK 74464, USA, e-mail:

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