In algebraic geometry, a morphism of schemes is called radicial or universally injective, if, for every field K the induced map X(K) → Y(K) is injective.
It suffices to check this for K algebraically closed.
This is equivalent to the following condition: f is injective on the topological spaces and for every point x in X, the extension of the residue fields is radicial, i.e. purely inseparable.
It is also equivalent to every base change of f being injective on the underlying topological spaces.
Radicial morphisms are stable under composition, products and base change.