If A' is a submodule of the right R-module A and B' is a submodule of the
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If A' is a submodule of the right R-module A and B' is a submodule of the left R-module B, then A/ A'⊗R B/B' ≅ (A⊗R B)/C, where C is the subgroup of A ⊗R B generated by all elements a' ⊗ b and a ⊗ b' with a ϵ A, a' ϵ A', b ϵ B, b' ϵ B'.
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ANSWER Lets begin by defining the maps that we will use to construct the isomorphism First we define a map A B AA R BB by sending aa bb to a A b B for ...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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