18 I : GENERAL THEORY

The freeness implies also R 0 f]{ h = ^ R 0 li for any family (Ii)i of ideals in A.

If we take as the U all ideals with Rg l{ D i7, then I = ^\iIi is the smallest ideal

of A with I' cR®I. Then

V C R ® ker(/?) ^=» Jcker(/3) *= /? e V(I)(B),

so

/-1OTor(5'p/c^,F/)

= !/(/) is closed.