Abstrakt
It is known that any finite idempotent algebra that satisfies a nontrivial Maltsev condition must satisfy the linear one-equality Maltsev condition (a variant of the term discovered by Siggers and refined by Kearnes, Markovi, and McKenzie): We show that if we drop the finiteness assumption, the k-ary weak near unanimity equations imply only trivial linear one-equality Maltsev conditions for every k3. From this it follows that there is no nontrivial linear one-equality condition that would hold in all idempotent algebras having Taylor terms.
Miroslav Olak has recently shown that there is a weakest nontrivial strong Maltsev condition for idempotent algebras. Olak has found several such (mutually equivalent) conditions consisting of two or more equations.
Our result shows that Olak's equation systems cannot be compressed into just one equation.