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# Generating Ideals in Rings of Integer-Valued Polynomials

Published:1999-06-01
Printed: Jun 1999
• David E. Rush
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## Abstract

Let $R$ be a one-dimensional locally analytically irreducible Noetherian domain with finite residue fields. In this note it is shown that if $I$ is a finitely generated ideal of the ring $\Int(R)$ of integer-valued polynomials such that for each $x \in R$ the ideal $I(x) =\{f(x) \mid f \in I\}$ is strongly $n$-generated, $n \geq 2$, then $I$ is $n$-generated, and some variations of this result.
 MSC Classifications: 13B25 - Polynomials over commutative rings [See also 11C08, 11T06, 13F20, 13M10] 13F20 - Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25] 13F05 - Dedekind, Prufer, Krull and Mori rings and their generalizations