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On the elasticities of Krull domains with finite cyclic divisor class group. (English) Zbl 0964.13001
Author’s abstract: Let \(R\) be a Krull domain with finite divisor class group \(\text{Cl}(R)\). We consider possible values of \(\rho(R)\), the elasticity of factorizations of \(R\). We first determine an upper bound on \(\rho(R)\) based on the distribution of height-one prime ideals in \(\text{Cl} (R)\) and characterize when this upper bound is attained. We concentrate on the case \(\text{Cl}(R) =\mathbb{Z}_{p^k}\), where \(p\) is a prime, and determine further bounds on \(\rho(R)\) when \(k=1\) (i.e., \(\text{Cl} (R)=\mathbb{Z}_p)\). Unlike a related analysis for the cross number of \(\mathbb{Z}_{p^k}\), we show that the elasticities of such domains do not take on a complete set of hypothesized values.

13A05 Divisibility and factorizations in commutative rings
13C20 Class groups
13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations
Full Text: DOI
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