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Keywords:
module; colimit; finitely presented module
Summary:
For every module $M$ we have a natural monomorphism \[ \Psi :\coprod _{i\in I}\mathop {\mathrm Hom}\nolimits _R(M,A_i)\rightarrow \mathop {\mathrm Hom}\nolimits _R\biggl (M,\coprod _{i\in I}A_i\biggr ) \] and we focus our attention on the case when $\Psi $ is also an epimorphism. Some other colimits are also considered.
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