statements are equivalent :
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![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
.....
......](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea9341d2-3bdf-4dd7-973b-08ac556e3a0a%2F6661a509-fd71-4c2e-9281-85279a7e96dc%2Fgh7oq6_processed.jpeg&w=3840&q=75)
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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