Relative Polynomial Closure and Monadically Krull Monoids of Integer-valued Polynomials
نویسنده
چکیده
Let D be a Krull domain and Int(D) the ring of integer-valued polynomials on D. For any f ∈ Int(D), we explicitly construct a divisor homomorphism from [[f ]], the divisor-closed submonoid of Int(D) generated by f , to a finite sum of copies of (N0,+). This implies that [[f ]] is a Krull monoid. For V a discrete valuation domain, we give explicit divisor theories of various submonoids of Int(V ). In the process, we modify the concept of polynomial closure in such a way that every subset of D has a finite polynomially dense subset. The results generalize to Int(S, V ), the ring of integer-valued polynomials on a subset, provided S doesn’t have isolated points in v-adic topology.
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