Elasticity of factorizations in atomic monoids and integral domains. (English) Zbl 0844.11068

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.


11R27 Units and factorization
13G05 Integral domains
13E05 Commutative Noetherian rings and modules
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