论文标题
胶状水平等于Alvin级别的一致性分布品种
The Gumm level equals the alvin level in congruence distributive varieties
论文作者
论文摘要
一致性模块化和一致性分布品种可以分别以Gumm和Jónsson项的序列存在。通常，此类序列具有可变的长度。从上面的段落中立即，有一个带有胶水术语的多样性，但没有jónsson术语。我们证明了一个非常出乎意料的结果，另一方面，如果某些品种都具有两种术语，那么序列的最小长度最少会差异为$ 1 $。因此，每一个$ r $模块化的一致性分配变体都是$ r^2-r+2 $ - 分布式。
Congruence modular and congruence distributive varieties can be characterized by the existence of sequences of Gumm and Jónsson terms, respectively. Such sequences have variable lengths, in general. It is immediate from the above paragraph that there is a variety with Gumm terms but without Jónsson terms. We prove the quite unexpected result that, on the other hand, if some variety has both kinds of terms, then the minimal lengths of the sequences differ at most by $1$. It follows that every $r$-modular congruence distributive variety is $r^2-r+2$-distributive.
