Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinite Easier Waring Constants for Commutative Rings   Suppose n >= 2. We show that there is no integer v >= 1 such that for all
commutative rings R with identity, every element of the subring J(2^n,R) of R
generated by 2^n-th powers can be written in the form \pm f_1^{2^n} \pm \cdots
\pm f_v^{2^n} for some f_1,...,f_v \in R and some choice of signs.

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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: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: supr-con