Abstract
In this note we show that if two critical algebras generate the same congruence-permutable variety, then the varieties generated by their proper sections also coincide.
Similar content being viewed by others
References
Bryant, R. M.,On S-critical groups, Quart. J. Math. Oxford22 (1971), 91–101.
Day, A. andKiss, E. W.,Frames and rings in congruence modular varieties, Journal of Algebra109 (1987), 479–507.
Freese, R.,On Jónsson's theorem, Algebra Universalis18 (1984), 70–76.
Freese, R. andMckenzie, R.,Commutator Theory for Congruence Modular Varieties, London Math. Soc. Lecture Notes Series, vol. 125, Cambridge University Press, 1987.
Gumm, H. P.,Geometrical methods in congruence modular algebras, Memoirs of the AMS45 (1983).
Jónsson, B.,Algebras whose congruence lattices are distributive, Math. Scand.21 (1967), 110–121.
Kiss, E. W.,On the Loewy rank of infinite algebras, Algebra Universalis29 (1992), 437–440.
Kovács, L. G. andNewman, M. F.,On critical groups, J. Austral Math. Soc. (1966), 237–250.
Mal'tsev, Yu. M.,Cross varieties of algebras, DAN SSSR278 (1984), 1060–1063.
Neumann, H.,Varieties of Groups, Springer-Verlag, Berlin, 1967.
Vovsi, S. M.,On locally finite varieties of group representations, Izv. VUZ Mat., 1971, No.6, 16–27.
Vovsi, S. M.,On critical multioperator groups, Sibirsk. Mat. Zh.30 (1989), 213–215.
Valeriote, M. A.,Finite simple Abelian algebras are strictly simple, Proceedings of the AMS108 (1990), 49–57.
Author information
Authors and Affiliations
Additional information
The research of the first author has been supported by the Hungarian National Foundation for Scientific Research (OTKA), grant number 1903.
Rights and permissions
About this article
Cite this article
Kiss, E.W., Vovsi, S.M. Critical algebras and the Frattini congruence. Algebra Universalis 34, 336–344 (1995). https://doi.org/10.1007/BF01182090
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01182090