Exercise 13, § 2

Commutative Algebra, I, 45

Bourbaki marks this one as harder than the rest.

Let A, B be two rings, F an (A, B)-bimodule and G a right B-module. Show that, if G is injective (Algebra Chapter II, § 2, Exercise 11) and F is a flat left A-module, the right A-module Hom_B(F, G) is injective. (Use the isomorphism

\operatorname{Hom}_A(E, \operatorname{Hom}_B(F, G)) \to \operatorname{Hom}_B(E \otimes_A F, G)

for a right A-module E (Algebra, Chapter II, § 4, no. 1).)

Solution

No solution has been written yet.