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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, 13F20, 13F05 show english descriptions Polynomials over commutative rings [See also 11C08, 11T06, 13F20, 13M10]
Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]
Dedekind, Prufer, Krull and Mori rings and their generalizations
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
 

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