吸收项和有向Jónsson项
Absorption and directed Jónsson terms
摘要：
证明了每一个同余分配簇都有有向Jónsson项，每一个同余模簇都有向Gumm项.我们构造的有向项见证了原始Jónsson或Gumm项所见证的每一种吸收情况。这一结果等价于CD和CM变种中关于可容许前序的吸收的一对主张。对于有限代数，这些吸收定理已经有了重要的应用，但直到现在，还不清楚这些定理是否也适用于一般代数。我们的方法还产生了一个新的证明结果P. Lipparini关于存在一个链的条款（我们称之为Pixley条款）的品种，在同一时间的同余分配和$k$ -置换的一些$k$。
英文摘要：
We prove that every congruence distributive variety has directed Jónsson terms, and every congruence modular variety has directed Gumm terms. The directed terms we construct witness every case of absorption witnessed by the original Jónsson or Gumm terms. This result is equivalent to a pair of claims about absorption for admissible preorders in CD and CM varieties, respectively. For finite algebras, these absorption theorems have already seen significant applications, but until now, it was not clear if the theorems hold for general algebras as well. Our method also yields a novel proof of a result by P. Lipparini about the existence a chain of terms (which we call Pixley terms) in varieties that are at the same time congruence distributive and $k$-permutable for some $k$.
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