An Order-Theoretic Property of the Commutator

@article{Kearnes1993AnOP,
  title={An Order-Theoretic Property of the Commutator},
  author={K. Kearnes},
  journal={Int. J. Algebra Comput.},
  year={1993},
  volume={3},
  pages={491-534}
}
  • K. Kearnes
  • Published 1993
  • Mathematics, Computer Science
  • Int. J. Algebra Comput.
We describe a new order-theoretic property of the commutator for finite algebras. As a corollary we show that any right nilpotent congruence on a finite algebra is left nilpotent. The result is false for infinite algebras and the converse is false even for finite algebras. We show further that any solvable E-minimal algebra is left nilpotent, any finite algebra whose congruence lattice contains a 0, 1-sublattice isomorphic to M3 is left nilpotent and any homomorphic image of a finite abelian… Expand
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