In algebraic geometry and commutative algebra, a ring homomorphism
Suppose B is given the structure of an A-algebra via the map f. Given a commutative A-algebra, C, and a nilpotent ideal
Formally smooth maps were defined by Alexander Grothendieck in Éléments de géométrie algébrique IV.
For finitely presented morphisms, formal smoothness is equivalent to usual notion of smoothness.