Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterization of Completions of Noncatenary Local Domains and
  Noncatenary Local UFDs   We find necessary and sufficient conditions for a complete local ring to be
the completion of a noncatenary local (Noetherian) domain, as well as necessary
and sufficient conditions for it to be the completion of a noncatenary local
(Noetherian) unique factorization domain. We use our first result to
demonstrate a large class of quasi-excellent domains that are not excellent, as
well as a large class of catenary domains that are not universally catenary. We
use our second result to find a larger class of noncatenary local UFDs than was
previously known, and we show that there is no bound on how noncatenary a UFD
can be.

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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga