Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abelian subcategories closed under extensions: K-theory and
  decompositions   A full subcategory of modules over a commutative ring $R$ is wide if it is
abelian and closed under extensions. Hovey \cite{wide} gave a classification of
wide subcategories of finitely presented modules over regular coherent rings in
terms of certain specialisation closed subsets of $\Spec(R)$. We use this
classification theorem to study K-theory and Krull-Schmidt type decompositions
for wide subcategories. It is shown that the K-group, in the sense of
Grothendieck, of a wide subcategory $\W$ of finitely presented modules over a
regular coherent ring is isomorphic to that of the thick subcategory of perfect
complexes whose homology groups belong to $\W$. We also show that the wide
subcategories of finitely generated modules over a noetherian regular ring can
be decomposed uniquely into indecomposable ones. This result is then applied to
obtain a decomposition for the K-groups of wide subcategories.

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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn