Critical algebras and the Frattini congruence
type: Item
instance of: scholarly article
title: Critical algebras and the Frattini congruence
zbMATH Open document ID: 0836.08006
DOI: 10.1007/BF01182090
author: Yanyan Li
published in: Algebra Universalis
publication date: 1996-01-23T00:00:00Z
review text: A finite algebra \(A\) is called critical if it does not belong to the variety \(SA\) generated by those homomorphic images of subalgebras of \(A\) that are not isomorphic to \(A\). The main purpose of the present paper is to show that \(SA = SB\) if the critical algebras \(A\) and \(B\) generate the same congruence-permutable variety; this generalizes the corresponding result on groups by \textit{R. M. Bryant} [Q. J. Math., Oxf., II. Ser. 22, 91-101 (1971; Zbl 0221.20036)].
reviewed by: Manfred Armbrust
Mathematics Subject Classification ID: 08B99
Mathematics Subject Classification ID: 08B10
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 836816
zbMATH Keywords: critical algebras
zbMATH Keywords: congruence-permutable variety
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 836816