To each 2-semilattice, one can associate a digraph and a partial order. We analyze these two structures working toward two main goals: One goal is to give a structural dichotomy on minimal congruences of 2-semilattices. From this, we are able to deduce information about the tame-congruence-theoretic types that occur in 2-semilattices. In particular, we show that the type of a finite simple 2-semilattice is always either 3 or 5 and can be deduced immediately from its associated digraph. The other goal is to introduce and explore a property that some 2-semilattices have which we have named the “component-semilattice property”. We show that this property must hold in every algebra in a variety of 2-semilattices that is both locally finite and residually small. Hence, a finite 2-semilattice that lacks this property generates a residually large variety.

对于每个2个半格，可以将一个有向图和一个偏序相关联。我们分析了实现两个主要目标的这两个结构：一个目标是对2-半字的最小全等给出结构二分法。据此，我们可以推断出关于2个半修饰出现的驯服同余理论类型的信息。特别是，我们证明了有限简单2半对称的类型始终为3或5并可以立即从其相关的有向图中推导出。另一个目标是引入和探索一些2个半修饰符具有的属性，我们将其命名为“ component-semilattice属性”。我们表明，该特性必须在局部有限且残差较小的2个半对称的所有代数中都成立。因此，缺少此特性的有限2半格会产生剩余的大量变化。