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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.

##### MSC:
 11R27 Units and factorization 13G05 Integral domains 13E05 Commutative Noetherian rings and modules
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##### References:
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