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Factorial groups and Pólya groups in Galoisian extension of \(\mathbb Q\). (English) Zbl 1107.13303
Fontana, Marco (ed.) et al., Commutative ring theory and applications. Proceedings of the fourth international conference, Fez, Morocco, June 7-12, 2001. New York, NY: Marcel Dekker (ISBN 0-8247-0855-5/pbk). Lect. Notes Pure Appl. Math. 231, 77-86 (2003).
Summary: The classical factorials in \(\mathbb{Z}\) may be generalized by factorial ideals in every integral domain \(D\). When \(D\) is completely integrally closed, these factorial ideals generate a subgroup of the divisorial group, the factorial group \(\text{Fact}(D)\), and, if \(D\) is a Krull domain, \(\text{Fact}(D)\) is a free abelian group. The classes of the factorial ideals generate the Pólya group \(\text{Po}(D)\) and we give some properties of this group \(\text{Po}(D)\), especially when \(D\) is the ring of integers of a finite Galoisian extension of \(\mathbb{Q}\).
For the entire collection see [Zbl 1027.00012].

13C20 Class groups
13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations
13F20 Polynomial rings and ideals; rings of integer-valued polynomials