Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal and cellular free resolutions over polynomial OI-algebras   Minimal free resolutions of graded modules over a noetherian polynomial ring
have been attractive objects of interest for more than a hundred years. We
introduce and study two natural extensions in the setting of graded modules
over a polynomial OI-algebra, namely minimal and width-wise minimal free
resolutions. A minimal free resolution of an OI-module can be characterized by
the fact that the free module in every fixed homological degree, say $i$, has
minimal rank among all free resolutions of the module. We show that any
finitely generated graded module over a noetherian polynomial OI-algebra admits
a graded minimal free resolution, and that it is unique. A width-wise minimal
free resolution is a free resolution that provides a minimal free resolution of
a module in every width. Such a resolution is necessarily minimal. Its
existence is not guaranteed. However, we show that certain monomial OI-ideals
do admit width-wise minimal free or, more generally, width-wise minimal flat
resolutions. These ideals include families of well-known monomial ideals such
as Ferrers ideals and squarefree strongly stable ideals. The arguments rely on
the theory of cellular resolutions.

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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas