Radicial morphism

In algebraic geometry, a domain in mathematics, a morphism of schemes:"f":"X" → "Y"is called radicial or universally injective, if, for every "g": "Y' "→"Y" the pullback of "f" along "g" is injective.

This is equivalent to the following condition: for every point "x" in "X", the extension of the residue fields:"k"("f"("x")) ⊂ "k"("x")is radicial, i.e. purely inseparable.

References

*, section I.3.5.
*, see section V.5.