Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transferring Davey`s Theorem on Annihilators in Bounded Distributive
  Lattices to Modular Congruence Lattices and Rings   Congruence lattices of semiprime algebras from semi--degenerate
congruence--modular varieties fulfill the equivalences from B. A. Davey`s
well--known characterization theorem for $m$--Stone bounded distributive
lattices, moreover, changing the cardinalities in those equivalent conditions
does not change their validity. I prove this by transferring Davey`s Theorem
from bounded distributive lattices to such congruence lattices through a
certain lattice morphism and using the fact that the codomain of that morphism
is a frame. Furthermore, these equivalent conditions are preserved by finite
direct products of such algebras, and similar equivalences are fulfilled by the
elements of semiprime commutative unitary rings and, dualized, by the elements
of complete residuated lattices.

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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: math-ph