Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Schr\"{o}der-Bernstein problem for Modules   In this paper we study the Schr\"{o}der-Bernstein problem for modules. We
obtain a positive solution for the Schr\"{o}der-Bernstein problem for modules
invariant under endomorphisms of their general envelopes under some mild
conditions that are always satisfied, for example, in the case of injective,
pure-injective or cotorsion envelopes. In the particular cases of injective
envelopes and pure-injective envelopes, we are able to extend it further and we
show that the Schr\"{o}der-Bernstein problem has a positive solution even for
modules that are invariant only under automorphisms of their injective
envelopes or pure-injective envelopes.

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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: plasm-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn