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Let M and M2 be two R-modules and N, and N2 be two submodules of M, and M2 respectively. Also, let f: M, an onto function defined by h(x + Ker(f)) = f(x) for x E M1. Then, M2 be a homomorphism and let h: M,/ker (f) → M2 be M1 = M2. M1/N1 = M2/N2 This option This option Nore of the choices M/Ker(f) M,

Let M and M2 be two R-modules and N, and N2 be two submodules of M, and M2 respectively. Also, let f: M, an onto function defined by h(x + Ker(f)) = f(x) for x E M1. Then, M2 be a homomorphism and let h: M,/ker (f) → M2 be M1 = M2. M1/N1 = M2/N2 This option This option Nore of the choices M/Ker(f) M,

Advanced Engineering Mathematics
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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Let M1 and M2 be two R-modules and N, and N2 be two submodules of M1 and M2 respectively. Also, let f: M, M2 be a homomorphism and let h: M1/ker (f) → M2 be an onto function defined by h(x + Ker(f)) = f(x) for x E M1. Then, M1 = M2. M1/N = M2/N2 This option This option None of the choices M/Ker(f) = M2
Transcribed Image Text:Let M1 and M2 be two R-modules and N, and N2 be two submodules of M1 and M2 respectively. Also, let f: M, M2 be a homomorphism and let h: M1/ker (f) → M2 be an onto function defined by h(x + Ker(f)) = f(x) for x E M1. Then, M1 = M2. M1/N = M2/N2 This option This option None of the choices M/Ker(f) = M2
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