Dimension of an integer valued polynomial ring
type: Item
instance of: scholarly article
title: Dimension of an integer valued polynomial ring
zbMATH Open document ID: 0712.13001
DOI: 10.1007/BF02568436
author: Paul-Jean Cahen
published in: Manuscripta Mathematica
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155503
review text: Let \(A\) be a commutative domain with quotient field \(K\). Define \(A_s=\{f\in K[X] \mid f(A)\subseteq A\}\), the ring of ``integer valued'' polynomials. The author shows that the Krull dimension of \(A_s\) satisfies the relation \(\dim (A_s)\ge \dim (A[X])-1\). He gives some examples where equality holds, and remarks that it is not known if strict inequality holds (non-trivially). He also gives a criterion for \(A_s\) to be different to \(A[X]\).
Mathematics Subject Classification ID: 13C15
Mathematics Subject Classification ID: 13B25
Mathematics Subject Classification ID: 13G05
zbMATH DE Number: 4171070
zbMATH Keywords: integer-valued polynomials
zbMATH Keywords: Krull dimension
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4171070