On ring homomorphisms
type: Item
instance of: scholarly article
title: On ring homomorphisms
zbMATH Open document ID: 0929.13011
author: Félix Cabello Sánchez
published in: Expositiones Mathematicae
publication date: 1999-12-02T00:00:00Z
review text: Let \({\mathbb R}[x]\) be the algebra of all polynomials in one indeterminate with real coefficients and \((x)\) be the ideal in \({\mathbb R}[x]\) generated by \(x\). It is shown that for each subring \(B\) of \({\mathbb R}\) containing \({\mathbb Q}\) there is a ring homomorphism from \((x)\) onto \(B\). From this it follows that all subfields of \({\mathbb R}\) containing \({\mathbb Q}\) are residual fields of \((x)\), not every prime ideal of \((x)\) is maximal, not all homomorphisms \((x)\to {\mathbb R}\) are \({\mathbb R}\)-linear (even if they are surjective) and \((x)\) is not a Noetherian ring.
reviewed by: Mati Abel
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 12D99
zbMATH DE Number: 1310294
zbMATH Keywords: real algebras
zbMATH Keywords: rings of polynomials
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1310294