完全解离广群
Completely dissociative groupoids
摘要：
考虑$k$变量$x_0, x_1, ..., x_{k-1}$上任意带括号的表达式，其中每个$x_i$只出现一次，并按其索引顺序出现。我们称这些表达式为{ \em形式$k$ --产品}。$F^σ(k)$表示形式$k$ --乘积的集合。对于${{\bf u},{\bf v}}\subseteq F^σ(k)$，对于变量$x_i$在$G$中假定的所有值，${\bf u}$和${\bf v}$在广群$G$中产生相等的元素的断言，将{ \em广义结合律}归于$G$。许多群胚是{ \em完全解离的};即，没有广义结合律对它们成立;两个例子是${0,1}$上的群胚，它们的二元运算是蕴涵和NAND。我们证明了各种结果的味道。
英文摘要：
Consider arbitrarily parenthesized expressions on the $k$ variables $x_0, x_1, ..., x_{k-1}$, where each $x_i$ appears exactly once and in the order of their indices. We call these expressions {\em formal $k$--products}. $F^σ(k)$ denotes the set of formal $k$--products. For ${{\bf u},{\bf v}}\subseteq F^σ(k)$, the claim, that ${\bf u}$ and ${\bf v}$ produce equal elements in a groupoid $G$ for all values assumed in $G$ by the variables $x_i$, attributes to $G$ a {\em generalized associative law}. Many groupoids are {\em completely dissociative}; i.e., no generalized associative law holds for them; two examples are the groupoids on ${0,1}$ whose binary operations are implication and NAND. We prove a variety of results of that flavor.
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