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.
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2 Pith papers cite this work. Polarity classification is still indexing.
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Cyclically pure subrings of Du Bois singularities are Du Bois over Q-algebras, with new results even for faithfully flat maps.
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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.
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Pure subrings of Du Bois singularities are Du Bois singularities
Cyclically pure subrings of Du Bois singularities are Du Bois over Q-algebras, with new results even for faithfully flat maps.