• Mathematics
  • Published 2000

Pure morphisms of commutative rings are effective descent morphisms for modules. A new proof.

@inproceedings{Mesablishvili2000PureMO,
  title={Pure morphisms of commutative rings are effective descent morphisms for modules. A new proof.},
  author={Bachuki Mesablishvili},
  year={2000}
}
The purpose of this paper is to give a new proof of the Joyal-Tierney theorem (unpublished), which asserts that a morphism f : R → S of commutative rings is an effective descent morphism for modules if and only if f is pure as a morphism of R-modules. Let R be a commutative ring with unit and R−mod the category of R-modules. Since, for any R-module M , the group C(M) = HomAb(M,Q/Z) (where Ab is the category of abelian groups and Q/Z is the rational circle abelian group) becomes an R-module with… CONTINUE READING

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