Integer-valued polynomials on a subset
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- by Paul-Jean Cahen PDF
- Proc. Amer. Math. Soc. 117 (1993), 919-929 Request permission
Abstract:
We let $D$ be a local (noetherian) one-dimensional unibranched domain, $K$ its quotient field, $\mathfrak {m}$ its maximal ideal, ${D’}$ its integral closure, and ${\mathfrak {m}’}$ the maximal ideal of ${D’}$. If $E$ is a subset of $K$, we let $\operatorname {Int} (E,D)$ be the set of integer-valued polynomials on $E$, thus $\operatorname {Int} (E,D) = \{ f \in K[X]|f(E) \subset D\}$. For a fractional subset $E$ of $D$ (i.e., there is a nonzero element $d$ of $D$ such that $dE \subset D$), we show that the prime ideals of $\operatorname {Int} (E,D)$ above $\mathfrak {m}$ are in one-to-one correspondence with the elements of the topological closure of $E$ in the completion of $K$ for the ${\mathfrak {m}’}$-adic topology.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 919-929
- MSC: Primary 13B25; Secondary 13F20, 13G05
- DOI: https://doi.org/10.1090/S0002-9939-1993-1116252-5
- MathSciNet review: 1116252