Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Similarity and commutators of matrices over principal ideal rings   We prove that if R is a principal ideal ring and A\in\M_n(R) is a matrix with
trace zero, then A is a commutator, that is, A=XY-YX for some X,Y\in\M_n(R).
This generalises the corresponding result over fields due to Albert and
Muckenhoupt, as well as that over Z due to Laffey and Reams, and as a
by-product we obtain new simplified proofs of these results. We also establish
a normal form for similarity classes of matrices over PIDs, generalising a
result of Laffey and Reams. This normal form is a main ingredient in the proof
of the result on commutators.

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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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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: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th