Restricted Elasticity and Rings of Integer-Valued Polynomials Determined by Finite Subsets

• Autores: Scott T. Chapman, William W. Smith
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 148, Nº 3, 2006, págs. 195-203
• Idioma: inglés
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• Resumen

  • Let D be an integral domain such that Int(D) ? K[X] where K is the quotient field of D. There is no known example of such a D so that Int(D) has finite elasticity. If E is a finite nonempty subset of D, then it is known that Int(E, D) = {f(X) ? K[X] | f(e) ? D for all e ? E} is not atomic. In this note, we restrict the notion of elasticity so that it is applicable to nonatomic domains. For each real number r = 1, we produce a ring of integer-valued polynomials with restricted elasticity r. We further show that if D is a unique factorization domain and E is finite with |E| > 1, then the restricted elasticity of Int(E, D) is infinite.