no. 2
Elasticity of factorizations in atomic monoids and integral domains
Journal de théorie des nombres de Bordeaux, Tome 7 (1995) no. 2, pp. 367-385.

L'élasticité ρ(R) d'un anneau d'intégrité atomique R est définie par : ρ ( R ) = sup { m / n | u 1 ⋯ u m = u 1 ⋯ v n pour u i et v j irréductibles dans ℝ } . Nous étudions ici l'élasticité des anneaux d'intégrité noethériens au moyen des invariants plus fins. Nous étudions ici l'élasticité des anneaux d'intégrité noethériens au moyen des invariants plus fins μ m (R) définis par : μ m ( R ) = sup { n | u 1 ⋯ u m = u 1 ⋯ v n pour u i et v j irréductibles dans R } . Le résultat principal que nous donnons permet de caractériser les anneaux d'entiers des corps de nombres qui ont une élasticité finie. Chemin faisant nous obtenons une série de résultats sur les invariants μ m et ρ des monoïdes et des anneaux d'intégrité qui ont un intérêt propre.

For an atomic domain R, its elasticity ρ(R) is defined by : ρ ( R ) = sup { m / n | u 1 ⋯ u m = v 1 ⋯ v n for irreducible u j , v i ∈ R } . We study the elasticity of one-dimensional noetherian domains by means of the more subtle invariants. We study the elasticity of one-dimensional noetherian domains by means of the more subtle invariants μ m (R) defined by : μ m ( R ) = sup { n | u 1 ⋯ u m = u 1 ⋯ v n for irreducible u j , v i ∈ R } . As a main result we characterize all orders in algebraic number fields having finite elasticity. On the way, we obtain a series of results concerning the invariants μ m and ρ for monoids and integral domains which are of independent interest.

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     title = {Elasticity of factorizations in atomic monoids and integral domains},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {367--385},
     publisher = {Universit\'e Bordeaux I},
     volume = {7},
     number = {2},
     year = {1995},
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Halter-Koch, Franz. Elasticity of factorizations in atomic monoids and integral domains. Journal de théorie des nombres de Bordeaux, Tome 7 (1995) no. 2, pp. 367-385. http://archive.numdam.org/item/JTNB_1995__7_2_367_0/

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