Bourbaki

Exercise 5, § 2

Commutative Algebra, I, 41

Give an example of a right A-module E, a left A-module F and two submodules F′,F′′F', F'' of F such that the canonical image of E⊗F′E \otimes F' and E⊗F′′E \otimes F'' in F′⊗F′′F' \otimes F'' is not the intersection of the canonical images of E⊗F′E \otimes F' and E⊗F′′E \otimes F'' in F′⊗F′′F' \otimes F'' (cf. Exercise 3(a)).

Solution

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Transcribed from the printed volume. Not translated.