Topological algebras with ascending or descending chain condition
type: Item
instance of: scholarly article
title: Topological algebras with ascending or descending chain condition
zbMATH Open document ID: 0939.46031
published in: Archiv der Mathematik
publication date: 2000-07-05T00:00:00Z
review text: All algebras under consideration are real and unital. An algebra is said to be Noetherian (resp. Artinian) if the family of all its left ideals satisfies the ascending (resp. descending) chain condition. The following main results are proved in this paper. (1) Every commutative Noetherian F-algebra is a Q-algebra. (2) Let \(A\) be a unitary F-algebra which is a Q-algebra. Then \(A\) is a Noetherian algebra if and only if every left ideal of \(A\) is closed. (3) Let \(A\) be a commutative normed algebra. Then \(A\) is finite-dimensional if and only if \(A\) is an Artianian algebra. Some other related results are also given.
Mathematics Subject Classification ID: 46H20
Mathematics Subject Classification ID: 13E10
Mathematics Subject Classification ID: 46H05
zbMATH DE Number: 1333332
zbMATH Keywords: left ideals
zbMATH Keywords: ascending (resp. descending) chain condition
zbMATH Keywords: Noetherian F-algebra
zbMATH Keywords: Q-algebra
zbMATH Keywords: Noetherian algebra
zbMATH Keywords: Artianian algebra
author: Rachid Choukri
author: A. El Kinani
reviewed by: Wong, Pak-ken
MaRDI profile type: Publication
full work available at URL: s000130050353
OpenAlex ID: W2008528325
DOI: 10.1007/S000130050353
description: scientific article; zbMATH DE number 1333332