Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gorenstein injective envelopes and covers over two sided noetherian
  rings   We prove that the class of Gorenstein injective modules is both enveloping
and covering over a two sided noetherian ring such that the character modules
of Gorenstein injective modules are Gorenstein flat. In the second part of the
paper we consider the connection between the Gorenstein injective modules and
the strongly cotorsion modules. We prove that when the ring R is commutative
noetherian of finite Krull dimension, the class of Gorenstein injective modules
coincides with that of strongly cotorsion modules if and only if the ring R is
in fact Gorenstein.

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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg