论文标题
完整的二进制树的代数已完成
The algebra of complete binary trees is affine complete
论文作者
论文摘要
代数上的功能是一致地保留的，如果任何一致性将一致的元素映射到一对元素成对上。我们表明，在完整的二进制树的代数上，其叶子被字母的字母标记为包含至少三个字母的字母，当且仅当它是多项式时，函数才能保留一个功能。这表明了非交换和非关联仿射完整代数的例子。据我们所知，这是这样的代数的第一个例子。
A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. We show that on the algebra of complete binary trees whose leaves are labeled by letters of an alphabet containing at least three letters a function is congruence preserving if and only if it is polynomial. This exhibits an example of a non commutative and non associative affine complete algebra. As far as we know, it is the first example of such an algebra.
