Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Lie nilpotent rings and Cohen's Theorem   We study certain (two-sided) nil ideals and nilpotent ideals in a Lie
nilpotent ring R. Our results lead us to showing that the prime radical rad(R)
of R comprises the nilpotent elements of R, and that if L is a left ideal of R,
then L+rad(R) is a two-sided ideal of R. This in turn leads to a Lie nilpotent
version of Cohen's theorem, namely if R is a Lie nilpotent ring and every prime
(two-sided) ideal of R is finitely generated as a left ideal, then every left
ideal of R containing the prime radical of R is finitely generated (as a left
ideal). For an arbitrary ring R with identity we also consider its so-called
n-th Lie center Z_n(R), which is a Lie nilpotent ring of index n. We prove that
if C is a commutative submonoid of the multiplicative monoid of R, then the
subring of R generated by the union of Z_n(R) and C is also Lie nilpotent of
index n.

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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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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: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph