Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal T-spaces of the free associative algebra over a finite field   In earlier work, it was established that for any finite field k, the free
associative k-algebra on one generator x, denoted by k[x]_0, had infinitely
many maximal T-spaces, but exactly two maximal $ideals (each of which is a
maximal T-space). However, aside from these two T-ideals, no examples of
maximal T-spaces of k[c]_0 have been identified. This paper presents, for each
finite field k, an infinite sequence of proper T-spaces of k[x]_0 (no one of
which is a T-ideal), each of finite codimension, and for each one, both a
linear basis for the T-space itself and a linear basis for a complementary
linear subspace are provided. Morever, it is proven that the first T-space in
the sequence is a maximal T-space of k[x]_0, thereby providing the first
example of a maximal T-space of k[x]_0 that is not a maximal T-ideal.

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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: physics