Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial bound for the nilpotency index of finitely generated nil
  algebras   Working over an infinite field of positive characteristic, an upper bound is
given for the nilpotency index of a finitely generated nil algebra of bounded
nil index $n$ in terms of the maximal degree in a minimal homogenous generating
system of the ring of simultaneous conjugation invariants of tuples of $n$ by
$n$ matrices. This is deduced from a result of Zubkov. As a consequence, a
recent degree bound due to Derksen and Makam for the generators of the ring of
matrix invariants yields an upper bound for the nilpotency index of a finitely
generated nil algebra that is polynomial in the number of generators and the
nil index. Furthermore, a characteristic free treatment is given to Kuzmin's
lower bound for the nilpotency index.

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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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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: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: physics