Article
Keywords:
uniformity; regularity; permutability; coherence; transferable congruences; Mal'cev condition
Summary:
An algebra $a$ is uniform if for each $\theta\in\Con a$, every two classes of $\theta$ have the same cardinality. It was shown by W. Taylor that coherent varieties need not be uniform (and vice versa). We show that every coherent variety having transferable congruences is uniform.
References:
[1] Chаjdа I.:
Transferable principal congruences and regular algebras. Math. Slovaca З4 (1984), 97-102.
MR 0735940
[3] Chаjdа I.:
Examples of local uniformity of congruences. Acta Sci. Math. (Szeged) 52 (1988), 81-84.
MR 0957790
[4] Chаjdа I:
Weak coherence of congruences. Czechoslovak Math. J. 41 (1991), 149-154.
MR 1087635
[5] Geiger D.: Coherent algebras. Notices Amer. Math. Soc. 21 (1974), 74T-A130.
[6] Krаuss P. H., Clаrk D. M.:
Global subdirect products. Mem. Amer. Math. Soc. 210 (1979).
MR 0512475
[9] Thurston H. A.:
Derived operations and congruences. Proc. London Math. Soc. 8 (1958), 127-134.
MR 0091924 |
Zbl 0078.01901