Bourbaki

Corollary

Tag 05PQ, permanent. Cite it as [Bourbaki, Tag 05PQ].

Algebra, chapter II, § 4. Relations between tensor products and homomorphism modules

If C is a commutative ring and E, F, G three C-modules, then the C-modules

HomC(E⊗CF,G),HomC(E,HomC(F,G)), \mathrm{Hom}_C(E \otimes_C F, G), \qquad \mathrm{Hom}_C(E, \mathrm{Hom}_C(F, G)),
HomC(F,HomC(E,G)),L2(E,F;G) \mathrm{Hom}_C(F, \mathrm{Hom}_C(E, G)), \qquad \mathscr{L}_2(E, F; G)
are canonically isomorphic.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Cites

Nothing.

Transcribed from the printed edition, 1998, Springer. Not translated.