Absorption and directed Jónsson terms

@article{Kazda2018AbsorptionAD,
  title={Absorption and directed J{\'o}nsson terms},
  author={Alexandr Kazda and Marcin Kozik and Ralph McKenzie and Matthew Moore},
  journal={arXiv: Rings and Algebras},
  year={2018},
  pages={203-220}
}
We prove that every congruence distributive variety has directed Jonsson terms, and every congruence modular variety has directed Gumm terms. The directed terms we construct witness every case of absorption witnessed by the original Jonsson or Gumm terms. This result is equivalent to a pair of claims about absorption for admissible preorders in congruence distributive and congruence modular varieties, respectively. For finite algebras, these absorption theorems have already seen significant… 
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