Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Absorption and directed J\'{o}nsson terms   We prove that every congruence distributive variety has directed J\'{o}nsson
terms, and every congruence modular variety has directed Gumm terms. The
directed terms we construct witness every case of absorption witnessed by the
original J\'{o}nsson 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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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics