Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Counterexample to a Question about Differential Ideals   This note intended to give a counterexample to a question related to the
following theorem. Let D be a differential domain finitely generated over a
differential field F with algebraically closed field of constants,C, of
characteristic 0. If D has no nonzero proper differential ideals, then the
differential constants of the quotient field of D is also C. The converse is
known to be false but the question of whether the differential domain D can be
finitely extended within its quotient field to a differential domain with no
nonzero proper differential ideals has been raised. A counterexample in the
case that F is infinitely generated over C has appeared. This paper intended to
give a counterexample in the case where F = C negating the natural question
whether adding the condition that F be finitely generated over C is sufficient
to guarantee a positive answer to the question. The question is still open.

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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: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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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: cond-mat
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The categories of this paper are: chao-dyn