Critical algebras and the Frattini congruence
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)].
scientific article; zbMATH DE number 836816