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statements are equivalent :

statements are equivalent :

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 1AEXP
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Theorem 6. Let M be an R-module and N,, N,.. N, be submodules of M. Then the fol- lowing statements are equivalent : (1) M = N, O N, O. ON ..... (ii) Ifn, + n, +. + n = 0, then n = n2 ..=n = 0 for n; e N; ..... ..... (iii) N;O (N, +.. + N + N; +1+..+ N) = {0} %3D ..... ......
Transcribed Image Text:Theorem 6. Let M be an R-module and N,, N,.. N, be submodules of M. Then the fol- lowing statements are equivalent : (1) M = N, O N, O. ON ..... (ii) Ifn, + n, +. + n = 0, then n = n2 ..=n = 0 for n; e N; ..... ..... (iii) N;O (N, +.. + N + N; +1+..+ N) = {0} %3D ..... ......
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