Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 71, No. 3, pp. 891-900, 2021

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

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

References:
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Affiliations: Richard Erwin Hasenauer, Northeastern State University, 600 N Grand Ave, Tahlequah, OK 74464, USA, e-mail: hasenaue@nsuok.edu

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