Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: co-Hopfian Modules   If $R$ is a ring with 1, we call a unital left $R$-module $M$ co-Hopfian
(Hopfian) in the category of left $R$-modules if any monic (epic) endomorphism
of $M$ is an automorphism. For commutative Noetherian $R$ we use results of
Matlis to show that in a certain context every submodule of a co-Hopfian
injective module is co-Hopfian. For these same $R,$ we characterize when a
finitely generated co-Hopfian module has finite length. We describe the
structure of Hopfian and co-Hopfian abelian groups whose torsion subgroup is
cotorsion.

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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin