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August 2016 About locally m-convex algebras with dense finitely generated ideals
Hugo Arizmendi Peimbert, Reyna María Pérez-Tiscareño
Ann. Funct. Anal. 7(3): 462-469 (August 2016). DOI: 10.1215/20088752-3605699

Abstract

It is well known, as a consequence of a theorem of Richard Arens, that a commutative Fréchet locally m-convex algebra E with unit does not have dense finitely generated ideals. We shall see that this result can no longer be true if E is not complete and metrizable. We observe that the same is true for the theorem of Arens; that is, this theorem can no longer be true if E is not complete and metrizable. Moreover, several conditions for a unital commutative (not necessarily complete) locally m-convex algebra are given, for which all maximal ideals have codimension one.

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Hugo Arizmendi Peimbert. Reyna María Pérez-Tiscareño. "About locally m-convex algebras with dense finitely generated ideals." Ann. Funct. Anal. 7 (3) 462 - 469, August 2016. https://doi.org/10.1215/20088752-3605699

Information

Received: 3 November 2015; Accepted: 26 January 2016; Published: August 2016
First available in Project Euclid: 19 July 2016

zbMATH: 1357.46041
MathSciNet: MR3528377
Digital Object Identifier: 10.1215/20088752-3605699

Subjects:
Primary: 46H05
Secondary: 46H20

Keywords: dense finitely generated ideals , locally $m$-convex algebra , theorem of Arens , Topological algebra

Rights: Copyright © 2016 Tusi Mathematical Research Group

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Vol.7 • No. 3 • August 2016
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