Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on completeness in the theory of strongly clean rings   Many authors have investigated the behavior of strong cleanness under certain
ring extensions. In this note, we prove that if $R$ is a ring which is complete
with respect to an ideal $I$ and if $x$ is an element of $R$ whose image in
$R/I$ is strongly $\pi$-regular, then $x$ is strongly clean in $R$.

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The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph