Let A,A 1 , ... , A n be R-modules. Then A A 1
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Let A,A1, ... , An be R-modules. Then A ≅ A1 ⊕ · · · ⊕ An if and only if for each i = 1,2, ... , n there is an R-module homomorphism ,φi : A → A such that Im φi ≅ Ai; φiφj = 0 for i ≠ j; and φi + ,φ2 + · · · + ,φn = 1A,
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The statement is known as the decomposition theorem for modules and it provides a necessary and suff...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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