Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integral Domains whose Simple Overrings are Intersections of
  Localizations   Call a domain $R$ an sQQR-domain if each simple overring of $R$, i.e., each
ring of the form $R[u]$ with $u$ in the quotient field of $R$, is an
intersection of localizations of $R$. We characterize Pr\"ufer domains as
integrally closed sQQR-domains. In the presence of certain finiteness
conditions, we show that the sQQR-property is very strong; for instance, a Mori
sQQR-domain must be a Dedekind domain. We also show how to construct
sQQR-domains which have (non-simple) overrings which are not intersections of
localizations.

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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: cs