Question: Let A, B, C be modules over a commutative ring R. (a) The set (A,B;C) of all R-bilinear maps A X B C is

Let A, B, C be modules over a commutative ring R.

(a) The set £(A,B;C) of all R-bilinear maps A X B → C is an R-module with (∫ + g)(a,b) = ∫(a,b) + g(a,b) and (r∫)(a,b) = r∫(a,b).

(b) Each one of the following R-modules is isomorphic to £(A,B;C):

(i) HomR(A ⊗R B,C);

(ii) HomR(A,HomR(B,C));

(iii) HomR(B,HomR(A,C)).

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