# Pure morphisms of commutative rings are effective descent morphisms for modules -- a new proof

## Bachuki Mesablishvili

The purpose of this paper is to give a new proof of the Joyal-Tierney theorem (unpublished), which asserts that a morphism $f:R\rightarrow S$ of commutative rings is an effective descent morphism for modules if and only if $f$ is pure as a morphism of $R$-modules.

Keywords: Pure morphisms,(effective) Descent morphisms, Split coequalizers.

2000 MSC: 13C99,18A20,18A30,18A40.

Theory and Applications of Categories, Vol. 7, 2000, No. 3, pp 38-42.

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