Elasticity of factorizations in atomic monoids and integral domains (Q1910676)

The elasticity \(\rho (R)\) of an atomic integral domain \(R\) is defined as the supremum of the ratios \(m/n\) taken over all equalities \(u_1 u_2 \dots u_m= v_1 v_2 \dots v_n\) with irreducible \(u_i\), \(v_j\). This notion is studied using the language of atomic monoids and it is shown that if \(R\) is a Krull domain, then \(\rho (R)\) depends only on the divisor class group of \(R\) and the set of divisor classes containing prime divisors. Also a characterization is given of orders in an algebraic number field which have finite elasticity.