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

Scott T. Chapman, William W. Smith

• 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.