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The Csákány theory of regularity for finite algebras. (English) Zbl 0844.08005
An algebra $$A$$ of which any two congruences coincide whenever they have a common class is called regular. The following theorem is proved:
Theorem. Let $$A$$ be a finite algebra with $$\text{card} (A)\leq 5$$. The following conditions are equivalent: (1) $$A$$ is regular; (2) there exists a ternary function $$p: A^3\to A$$ compatible with every congruence of $$A$$ such that $$p(x, y, z)= z\Leftrightarrow x=y$$.
This is not true for six-element algebras.
##### MSC:
 08A30 Subalgebras, congruence relations
##### Keywords:
regular algebra; term condition
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##### References:
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