Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalizations of the Direct Summand Theorem over UFD-s for some
  Bigenerated Extensions and an Asymptotic Version of Koh's Conjecture   This article deals with two different problems in commutative algebra. In the
first part, we give a proof of generalized forms of the Direct Summand Theorem
(DST (or DCS)) for module-finite extension rings of mixed characteristic
$R\subset S$ satisfying the following hypotheses: The base ring $R$ is a Unique
Factorization Domain of mixed characteristic zero. We assume that $S$ is
generated by two elements which satisfy, either radical quadratic equations, or
general quadratic equations under certain arithmetical restrictions. In the
second part of this article, we discuss an asymptotic version of Koh's
Conjecture. We give a model theoretical proof using "non-standard methods".

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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: nlin