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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.

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