Taylor项不包含任何非平凡的线性一等Maltsev条件
Taylor term does not imply any nontrivial linear one-equality Maltsev condition
摘要：
已知任何满足非平凡Maltsev条件的有限幂等代数必须满足线性一等Maltsev条件（M. Siggers和改进的K。Kearnes、P. Marković和R. McKenzie）：\[ t(r,a,r,e)\approx t(a,r,e,a). \]我们证明了，如果我们放弃有限性假设，$k$元弱拟线性方程对每一个$k\geq 3$只蕴涵平凡的线性一等Maltsev条件.从这一点可以得出，没有非平凡的线性一等式条件，将保持在所有幂等代数泰勒项。Miroslav Olšák最近证明了幂等代数存在一个最弱的非平凡强Maltsev条件。Olšák发现了几个这样的（相互等价的）条件，由两个或更多的方程组成。结果表明，Olšák方程组不能压缩为一个方程.
英文摘要：
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 M. Siggers and refined by K. Kearnes, P. Marković, and R. McKenzie): \[ t(r,a,r,e)\approx t(a,r,e,a). \] 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 $k\geq 3$. From this it follows that there is no nontrivial linear one-equality condition that would hold in all idempotent algebras having Taylor terms. Miroslav Olšák has recently shown that there is a weakest nontrivial strong Maltsev condition for idempotent algebras. Olšák has found several such (mutually equivalent) conditions consisting of two or more equations. Our result shows that Olšák's equation systems can't be compressed into just one equation.
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