More generally, for a scheme "X" over a commutative ring "R" and any commutative "R"-algebra "S", an "S"-point of "X" means a morphism Spec("S") → "X" over "R". One writes "X"("S") for the set of "S"-points of "X". (This generalizes the old observation that given some equations over a field "k", one can consider the set of solutions of the equations in any field extension "E" of "k".) For a scheme "X" over "R", the assignment "S" ↦ "X"("S") is a functor from commutative "R"-algebras to sets. It is an important observation that a scheme "X" over "R" is determined by this functor of points.