Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reticulation functor and the transfer properties   It is known that by using the commutator operation, for each congruence
modular algebra $A$ one can define a notion of prime congruence. The set
$Spec(A)$ of prime congruences of $A$ is endowed with a Zariski style topology.
The reticulation of the algebra $A$ is a bounded distributive lattice $L(A)$
whose prime spectrum $Spec(L(A))$ (with the Stone topology) is homemorphic to
$Spec(A)$.
  In a recent paper, C. Mure\c{s}an and the author have proven the existence of
reticulation for a semidegenerate congruence modular algebra $A$.
  The present paper aims to give an answer to two types of problems:
  $(I)$ how some properties of the algebra $A$ can be transferred to the
lattice $L(A)$ and viceversa, how some properties of $L(A)$ can be transferred
to $A$;
  $(II)$ how the transfer properties from $(I)$ can be used to prove some old
and new characterizations of some remarkable classes of algebras.
  We study the transfer properties related to Boolean centers, annihilators,
patch and flat topologies of spectra, Pierce spectrum, pure and $w$ - pure
congruences, the operators $Ker(\cdot)$ and $O(\cdot)$,etc.
  By using these transfer properties, we obtain characterization theorems for
several types of algebras : hyperarchimedean algebras, congruence normal and
congruence $B$ - normal algebras, $mp$ - algebras, $PF$ - algebras, congruence
purified algebras and $PP$ - algebras.

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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex