容许关系的并
Unions of admissible relations
摘要：
证明了一个簇$\mathcal V$是同余分配的当且仅当存在一些$h$使得包含（1）$Θ\cap ( σ\circ σ) \subseteq ( Θ\cap σ) \circ ( Θ\cap σ) \circ \dots $（$h$因子）对每个容差$Θ$和每个U-容许关系$σ$在$\mathcal V$的每个代数中成立.通过U-容许关系，我们指的是二元关系，它是一组自反和容许关系的集合论并集。对于任何固定的$h$，对于包含体（1）给出Maltsev型特征。当假定$Θ$是$U$ -容许关系而不是容许关系时，（1）是否仍然等价于同余分配是一个公开问题.在这两种情况下，给出了（1）的许多等价公式。结果表明，它可能是有趣的，以研究的结构的集合上的U-容许关系的代数，以及处理这种关系的身份。
英文摘要：
We show that a variety $\mathcal V$ is congruence distributive if and only if there is some $h$ such that the inclusion (1) $Θ\cap ( σ\circ σ) \subseteq ( Θ\cap σ) \circ ( Θ\cap σ) \circ \dots $ ($h$ factors) holds in every algebra in $\mathcal V$, for every tolerance $Θ$ and every U-admissible relation $σ$. By a U-admissible relation we mean a binary relation which is the set-theoretical union of a set of reflexive and admissible relations. For any fixed $h$, a Maltsev-type characterization is given for the inclusion (1). It is an open problem whether (1) is still equivalent to congruence distributivity when $Θ$ is assumed to be a $U$-admissible relation, rather than a tolerance. In both cases many equivalent formulations for (1) are presented. The results suggest that it might be interesting to study the structure of the set of U-admissible relations on an algebra, as well as identities dealing with such relations.
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