A Noetherian ring R is a splinter if and only if every equidimensional surjective morphism Spec(S) to Spec(R) makes R to S pure.
Algebraic Geom
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Equidimensional morphisms onto splinters are pure
A Noetherian ring R is a splinter if and only if every equidimensional surjective morphism Spec(S) to Spec(R) makes R to S pure.