论文标题
统一的一致性和一元代数
Profinite congruences and unary algebras
论文作者
论文摘要
很难描述涂鸦代数的概括性代数。特别是，尚无建设性描述，即在代数上包含给定的二进制关系的最少属性一致性。另一方面，可以建设性地描述封闭的一致性和完全不变的一致性。在上一篇论文中，我们猜想完全不变的封闭一致性相对自由的代数始终是涂鸦。在这里，我们表明我们的猜想失败了一元代数，并且对相对自由的半群的封闭一致性不一定是涂鸦。作为我们对单一代数的研究的一部分，我们建立了斑点的一元代数和涂鸦单素之间的邻接。我们还表明，波兰自由的单一代数的代表是忠实的。
Profinite congruences on profinite algebras determining profinite quotients are difficult to describe. In particular, no constructive description is known of the least profinite congruence containing a given binary relation on the algebra. On the other hand, closed congruences and fully invariant congruences can be described constructively. In a previous paper, we conjectured that fully invariant closed congruences on a relatively free profinite algebra are always profinite. Here, we show that our conjecture fails for unary algebras and that closed congruences on relatively free profinite semigroups are not necessarily profinite. As part of our study of unary algebras, we establish an adjunction between profinite unary algebras and profinite monoids. We also show that the Polish representation of the free profinite unary algebra is faithful.
