Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: FI- and OI-modules with varying coefficients   We introduce FI-algebras over a commutative ring $K$ and the category of
FI-modules over an FI-algebra. Such a module may be considered as a family of
invariant modules over compatible varying $K$-algebras. FI-modules over $K$
correspond to the well studied constant coefficient case where every algebra
equals $K$. We show that a finitely generated FI-module over a noetherian
polynomial FI-algebra is a noetherian module. This is established by
introducing OI-modules. We prove that every submodule of a finitely generated
free OI-module over a noetherian polynomial OI-algebra has a finite Gr\"obner
basis. Applying our noetherianity results to a family of free resolutions,
finite generation translates into stabilization of syzygies in any fixed
homological degree. In particular, in the graded case this gives uniformity
results on degrees of minimal syzygies.

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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: stat