Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The finite basis problem for the monoid of 2 by 2 upper triangular
  tropical matrices   For each positive $n$, let $u_n = v_n$ denote the identity obtained from the
Adjan identity $(xy) (yx) (xy) (xy) (yx) = (xy) (yx) (yx) (xy) (yx)$ by
substituting $(xy) \rightarrow (x_1 x_2 \dots x_n)$ and $(yx) \rightarrow (x_n
\dots x_2 x_1)$. We show that every monoid which satisfies $u_n = v_n$ for each
positive $n$ and generates the variety containing the bicyclic monoid is
nonfinitely based.
  This implies that the monoid of 2 by 2 upper triangular tropical matrices
over the tropical semiring is nonfinitely based.

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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph