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Elasticity for integral-valued polynomials. (English) Zbl 0843.12001

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 \(u_i\), \(v_j\). The authors exhibit large classes of domains with infinite elasticity. This includes in particular \(\text{Int} (D)\), the ring of all \(D\)-valued polynomials for one-dimensional Noetherian domain \(D\) with finite residue fields.

MSC:

12E05 Polynomials in general fields (irreducibility, etc.)
13G05 Integral domains
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
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References:

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