Elasticities of Krull domains with finite divisor class group
For an atomic domain \(R\), the elasticity \(\rho(R)\) of \(R\) is defined by \[ \rho(R)=\sup\{m/n\mid a_1\cdots a_m=b_1\cdots b_n \text{ for some irreducibles }a_i,b_j\in R\}. \] Let \(G\) be a finite abelian group. Then \({\mathcal Y}(G)\) denotes the set of all values \(\rho(R)\), where \(R\) ranges among all Krull domains with divisor class group \(G\). In this paper, the author studies \({\mathcal Y}(G)\) for some special finite abelian groups \(G\) of the form \({\mathbb Z}_p,\;\mathbb Z_{2p}\), where \(p\) is a prime integer. He also shows that \({\mathcal Y}(\bigoplus_{i=1}^k\mathbb Z_2)=\{1,3/2,4/2,\ldots,(k+1)/2\}\), for any positive integer \(k\).
scientific article; zbMATH DE number 2083499