Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modules with Pure Resolutions   We show that the property of a standard graded algebra R being Cohen-Macaulay
is characterized by the existence of a pure Cohen-Macaulay R-module
corresponding to any degree sequence of length at most depth(R). We also give a
relation in terms of graded Betti numbers, called the Herzog-Kuhl equations,
for a pure R-module M to satisfy the condition dim(R) - depth(R) = dim(M) -
depth(M). When R is Cohen-Macaulay, we prove an analogous result characterizing
all graded Cohen-Macaulay R-modules.

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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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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: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg