A Note on Flat Algebras

Abstract

Abstract. The following results are proved. If /: A -> B is a homomorphism of rings, with B noetherian, / is an ideal of B contained in the Jacobson radical, and B/I" is A -flat, for all n, then/is flat. If, using similar notations and assumptions, / is generated by a regular sequence, then the flatness of B/I implies the flatness of/. A simple geometric application is given.