Commutative rings and binomial coefficients
type: Item
instance of: scholarly article
title: Commutative rings and binomial coefficients
zbMATH Open document ID: 0764.12002
DOI: 10.1007/BF01535576
author: Franz Halter-Koch
author: Władysław Narkiewicz
published in: Monatshefte für Mathematik
publication date: 1993-05-12T00:00:00Z
full work available at URL: https://eudml.org/doc/178578
review text: Let \(R\) be a domain with quotient field \(k\) and let \(S(R)\) be the \(R\)- module of all \(k\)-polynomials mapping \(R\) in \(R\). It has been shown by \textit{G. Pólya} [Rend. Circ. Mat. Palermo 40, 1-16 (1915; JFM 45.0655.02)] that \(S(Z)\) is generated by binomial coefficients. \textit{G. Gerboud} [C. R. Acad. Sci., Paris, Sér. A 307, 1-4 (1988; Zbl 0656.13022)] found other such domains. Here all domains \(R\) with this property are described. In particular a Noetherian domain \(R\) has this property if and only if for every rational prime \(p\) non-invertible in \(R\) the ideal \(pR\) is a product of distinct prime ideals of index \(p\).
reviewed by: Franz Halter-Koch
Mathematics Subject Classification ID: 12E05
Mathematics Subject Classification ID: 13G05
Mathematics Subject Classification ID: 13B25
zbMATH DE Number: 164915
zbMATH Keywords: polynomial maps
zbMATH Keywords: binomial coefficients
zbMATH Keywords: Noetherian domain
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 164915