On the congruences of the direct product of algebra
Algebra i logika, Tome 6 (1967) no. 1, pp. 39-43
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An example is given of the direct product $\mathscr{O}\times\mathscr{L}$ of two simple algebras $\mathscr{O}$, $\mathscr{L}$ (of $2$ and $3$ order), where the lattice of congruences is modular and the congruences are not permutable.
@article{AL_1967_6_1_a4,
author = {A. F. Bravcev},
title = {On the congruences of the direct product of algebra},
journal = {Algebra i logika},
pages = {39--43},
publisher = {mathdoc},
volume = {6},
number = {1},
year = {1967},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/AL_1967_6_1_a4/}
}
A. F. Bravcev. On the congruences of the direct product of algebra. Algebra i logika, Tome 6 (1967) no. 1, pp. 39-43. http://geodesic.mathdoc.fr/item/AL_1967_6_1_a4/