Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The socle module of a monomial ideal   For any ideal $I$ in a Noetherian local ring or any graded ideal $I$ in a
standard graded $K$-algebra over a field $K$, we introduce the socle module
$\mathrm{Soc}(I)$, whose graded components give us the socle of the powers of
$I$. It is observed that $\mathrm{Soc}(I)$ is a finitely generated module over
the fiber cone of $I$. In the case that $S$ is the polynomial ring and all
powers of $I\subseteq S$ have linear resolution, we define the module
$\mathrm{Soc}^*(I)$ which is a module over the Rees ring of $I$. For the edge
ideal of a graph and for classes of polymatroidal ideals we study the module
structure of their socle modules.

15
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: bayes-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
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The categories of this paper are: econ
6
The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph