Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Contraadjusted modules, contramodules, and reduced cotorsion modules   This paper is devoted to the more elementary aspects of the contramodule
story, and can be viewed as an extended introduction to the more technically
complicated arXiv:1503.05523. Reduced cotorsion abelian groups form an abelian
category, which is in some sense covariantly dual to the category of torsion
abelian groups. An abelian group is reduced cotorsion if and only if it is
isomorphic to a product of p-contramodule abelian groups over prime numbers p.
Any p-contraadjusted abelian group is p-adically complete, and any p-adically
separated and complete group is a p-contramodule, but the converse assertions
are not true. In some form, these results hold for modules over arbitrary
commutative rings, while other formulations are applicable to modules over
one-dimensional Noetherian rings.

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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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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: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph