ИСТИНА

In 2005 M.Maroti proved that having a near-unanimity term operation (NU) is a decidable property of a finite algebra, but he didn't give any upper bound on the minimal arity of NU. In 2013 D.Zhuk obtained an upper bound, which automatically gives an algorithm to decide the property. Precisely, he showed that a finite algebra with NU has NU of arity at most |A|2·(|A|·m)(3|A|)|A|, where m is the maximal arity of fundamental operations. We improved this result and showed that m|A|3/2 is an upper bound, and (m-1)|A|(|A|-1)/2+1 is an upper bound for idempotent algebras. Moreover, we proved for a finite idempotent algebra (A;f1, ..., fs) with NU that it has NU of arity at most 1+∑i=1s(arity(fi)-1), and showed that both upper bounds for idempotent algebras cannot be improved.