Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Koszulity of algebras with non-pure resolutions   We discuss certain homological properties of graded algebras whose trivial
modules admit non-pure resolutions. Such algebras include both of
Artin-Schelter regular algebras of types (12221) and (13431). Under certain
conditions, a module with non-pure resolution is decomposed to form an
extension by two modules with pure resolutions.

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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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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: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn