When is \(C(X)\) polynomially ideal?
type: Item
instance of: scholarly article
title: When is \(C(X)\) polynomially ideal?
zbMATH Open document ID: 1352.13002
DOI: 10.1216/JCA-2015-7-4-473
author: Karim Boulabiar
author: Samir Smiti
published in: Journal of Commutative Algebra
publication date: 2016-01-21T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.jca/1453211670
review text: For an \(f\)-algebra and an ideal \(\mathfrak a\), a notion of being polynomially \(\mathfrak a\)-ideal is introduced. It is shown that if the algebra is bounded inversion closed and \(\mathfrak a\) is an intersection of maximal ideals, this notion is equivalent to idempotents lifting modulo \(\mathfrak a\). For spaces of continuous functions on a Tychonoff space, the notion is then linked to the space being a \(P\)-space and being strongly zero-dimensional.
reviewed by: Tim Netzer
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 46E25
Mathematics Subject Classification ID: 06F25
Mathematics Subject Classification ID: 16W80
zbMATH DE Number: 6533977
zbMATH Keywords: commutative \(f\)-algebra
zbMATH Keywords: idempotent element
zbMATH Keywords: polynomially ideal
zbMATH Keywords: intersection of maximal ideals
zbMATH Keywords: completely regular space
zbMATH Keywords: lattice-ordered algebra
MaRDI profile type: Publication
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OpenAlex ID: W2290692759
description: scientific article; zbMATH DE number 6533977