Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Upper Bound for the First Hilbert Coefficient of Gorenstein Algebras
  and Modules   Let $R$ be a polynomial ring over a field and $M= \bigoplus_n M_n$ a finitely
generated graded $R$-module, minimally generated by homogeneous elements of
degree zero with a graded $R$-minimal free resolution $\mathbf{F}$. A
Cohen-Macaulay module $M$ is Gorenstein when the graded resolution is
symmetric. We give an upper bound for the first Hilbert coefficient, $e_1$ in
terms of the shifts in the graded resolution of $M$. When $M = R/I$, a
Gorenstein algebra, this bound agrees with the bound obtained in \cite{ES} in
Gorenstein algebras with quasi-pure resolution. We conjecture a similar bound
for the higher coefficients.

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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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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: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: eess