Talk:Integer-valued polynomial

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Numbers

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suggested merger

This article should be merged into numerical polynomial. Numerical polynomial is the more common term, but it means the exact same thing.--345Kai (talk) 22:58, 2 February 2010 (UTC)[reply]

Why do you say that term is more common? Charles Matthews (talk) 08:12, 3 February 2010 (UTC)[reply]

If they are the same thing, which looks like it is the case, the articles should be merged. However, I strongly doubt the term "numerical polynomial" is more common, as it transmits absolutely nothing about the concept. I would have guessed a numerical polynomial is a polynomial with numerical coefficients. Doing a google scholar search not only seems to confirm that "integer valued polynomial" is more common, as in this title, it also returns this reference that defines numerical polynomials as those taking natural number values on sufficiently large natural numbers, which is a more limited notion. Marc van Leeuwen (talk) 11:41, 29 March 2011 (UTC)[reply]

Merger to be completed shortly. --Joel B. Lewis (talk) 00:51, 27 March 2012 (UTC)[reply]

Why almost no algebraic properties of this ring are mentioned?

Let $\operatorname {Int} (\mathbb {Z} )$ be the ring of integer-valued polynomials.

$\operatorname {Int} (\mathbb {Z} )$ is a Prüfer domain: see here.

$\operatorname {Int} (\mathbb {Z} )$ is not a GCD domain, since Prüfer domain + GCD domain is equivalent to Bézout domain (mentioned in the Wikipedia page; see also here), and $\operatorname {Int} (\mathbb {Z} )$ is clearly not a Bézout domain as $(2,X)$ is not principal.

$\operatorname {Int} (\mathbb {Z} )$ is not a Dedekind domain (or equivalently, not a Noetherian domain).

$\operatorname {Int} (\mathbb {Z} )$ is an atomic domain: see here. 129.104.241.34 (talk) 01:15, 30 November 2024 (UTC)[reply]