Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rings without a Gorenstein analogue of the Govorov-Lazard Theorem   It was proved by Beligiannis and Krause that over certain Artin algebras,
there are Gorenstein flat modules which are not direct limits of finitely
generated Gorenstein projective modules. That is, these algebras have no
Gorenstein analogue of the Govorov-Lazard Theorem.
  We show that, in fact, there is a large class of rings without such an
analogue. Namely, let R be a commutative local noetherian ring. Then the
analogue fails for R if it has a dualizing complex, is henselian, not
Gorenstein, and has a finitely generated Gorenstein projective module which is
not free.
  The proof is based on a theory of Gorenstein projective (pre)envelopes. We
show, among other things, that the finitely generated Gorenstein projective
modules form an enveloping class in mod R if and only if R is Gorenstein or has
the property that each finitely generated Gorenstein projective module is free.
  This is analogous to a recent result on covers by Christensen, Piepmeyer,
Striuli, and Takahashi, and their methods are an important input to our work.

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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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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: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys