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Additional info for An Introduction to Galois Theory [Lecture notes]
Show that if N is a left R-module then as an abelian group S ⊗R N ∼ = N d with isomorphism induced from (s1 r1 + · · · + sd rd ) ⊗ n = si ⊗ (ri n) → (r1 n, r2 n, . . rd n).
Sd . Show that if N is a left R-module then as an abelian group S ⊗R N ∼ = N d with isomorphism induced from (s1 r1 + · · · + sd rd ) ⊗ n = si ⊗ (ri n) → (r1 n, r2 n, . . rd n).