On function algebras in which every congruence is determined by a filter
type: Item
instance of: scholarly article
title: On function algebras in which every congruence is determined by a filter
zbMATH Open document ID: 0731.08002
DOI: 10.1016/0022-4049(90)90047-L
author: N. E. Zubov
published in: Journal of Pure and Applied Algebra
publication date: 1990-01-01T00:00:00Z
review text: It is proved that for certain universal algebras A there is a bijection between the congruences on \(A^ X\) and the filters on X. From this result a description of all left ideals of the near-ring of all functions of a group G to itself is obtained. Moreover, the well-known result concerning the simplicity of this near-ring for \(| G| >2\) follows almost immediately. Finally, function algebras are studied, where every invariant subalgebra is determined by its image.
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 16Y30
zbMATH DE Number: 4208133
zbMATH Keywords: congruence relation
zbMATH Keywords: filters
zbMATH Keywords: near-ring
zbMATH Keywords: function algebras
reviewed by: Helmut Länger
MaRDI profile type: Publication
cites work: Simplicity of Near-Rings of Transformations
cites work: Q4405046
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cites work: Q5808059
cites work: Adequate subcategories
cites work: Right ideals and right submodules of transformation near-rings
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cites work: Q3692879
cites work: Finitely Generated Right Ideals of Transformation Near-Rings
full work available at URL: 0022-4049(90)90047-l
OpenAlex ID: W2019167102
description: scientific article; zbMATH DE number 4208133