Geodesic
PERMUTABILITY OF TOLERANCES WITH FACTOR AND DECOMPOSING CONGRUENCES
Acta mathematica Universitatis Comenianae, Tome 65 (1996) no. 1 
I. Chajda. PERMUTABILITY OF TOLERANCES WITH FACTOR AND DECOMPOSING CONGRUENCES. Acta mathematica Universitatis Comenianae, Tome 65 (1996) no. 1. http://geodesic.mathdoc.fr/item/AMUC_1996_65_1_a7/
@article{AMUC_1996_65_1_a7,
     author = {I. Chajda},
     title = {PERMUTABILITY {OF} {TOLERANCES} {WITH} {FACTOR} {AND} {DECOMPOSING} {CONGRUENCES}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {1996},
     volume = {65},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_1996_65_1_a7/}
}
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Voir la notice de l'article provenant de la source Comenius University

A variety $\vv$ has tolerances permutable with factor congruences if for any $A_1,A_2$ of $\vv$ and every tolerance $T$ on $A_1 \times A_2$ we have $T \circ \Pi_1 =\Pi_1 \circ T$ and $T \circ \Pi_2 =\Pi_2 \circ T$, where $\Pi_1,\Pi_2$ are factor congruences. If $B$ is a subalgebra of $A_1 \times A_2$, the congruences $\Theta_i= \Pi_i \cap B^2$ are called decomposing congruences. $\vv$ has tolerances permutable with decomposing congruences if $T \circ \Theta_i =\Theta_i \circ T$ $(i=1,2)$ for each $A_1,A_2 \in \vv$, every subalgebra $B$ of $A_1 \times A_2$ and any tolerance $T$ on $B$. The paper contains Mal'cev type condition characterizing these varieties.