Let be a free Z-module with an infinite basis X. Then { x |x X} .nX
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Let be a free Z-module with an infinite basis X. Then {∫x|x ϵ X} .nX (Theorem 4.11) does not form a basis of F*.
Data from theorem 4.11
(i) If fx1rl + fx2r2+ ... + fxnrn = 0 (ri e R; Xi eX), then for each j = 0, 1,2, ... , n,
Transcribed Image Text:
F - Σ Z Zx reX
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xj fxjrj 0 ii If fx1rl fx2r2 fxnrn 0 ri e Z Xi e X then f 0 Based on the information provided it ...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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