Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The norm of a skew polynomial   Let $D$ be a finite-dimensional division algebra over its center and
$R=D[t;\sigma,\delta]$ a skew polynomial ring. Under certain assumptions on
$\delta$ and $\sigma$, the ring of central quotients $D(t;\sigma,\delta) =
\{f/g \,|\, f \in D[t;\sigma,\delta], g \in C(D[t;\sigma,\delta])\}$ of
$D[t;\sigma,\delta]$ is a central simple algebra with reduced norm $N$. We
calculate the norm $N(f)$ for some skew polynomials $f\in R$ and investigate
when and how the reducibility of $N(f)$ reflects the reducibility of $f$.

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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol