Let A, B, C be modules over a commutative ring R. (a) The set (A,B;C) of all
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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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a To show that the set A B C of all Rbilinear maps A x B C is an Rmodule we need to verify that it s...View the full answer
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Related Book For 
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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