Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Note on the Buchsbaum-Rim function of a parameter module   In this article, we prove that the Buchsbaum-Rim function
$\ell_A(\S_{\nu+1}(F)/N^{\nu+1})$ of a parameter module $N$ in $F$ is bounded
above by $e(F/N) \binom{\nu+d+r-1}{d+r-1}$ for every integer $\nu \geq 0$.
Moreover, it turns out that the base ring $A$ is Cohen-Macaulay once the
equality holds for some integer $\nu$. As a direct consequence, we observe that
the first Buchsbaum-Rim coefficient $e_1(F/N)$ of a parameter module $N$ is
always non-positive.

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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph