hese problems let R be any ring and Mand N R- orem A: If ƒ :M → N is an R- module epimom Kerf≈ N (this is the FHT for modules)
hese problems let R be any ring and Mand N R- orem A: If ƒ :M → N is an R- module epimom Kerf≈ N (this is the FHT for modules)
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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Abstract algebra 2. Graduate level
![**Mathematical Problem: Fundamental Theorem of Homomorphisms for Modules**
In all these problems, let \( R \) be any ring and \( M \) and \( N \) be \( R \)-modules.
1. **Theorem A**: If \( f : M \to N \) is an \( R \)-module epimorphism, **PROVE**:
\[
M/\text{Ker} f \cong N
\]
(this is the FHT for modules)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F32f77ee0-291c-46d0-b315-80fb2fd096d8%2F6ed29473-47f1-41a9-b55c-be64e3121eed%2Fpyidmbr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Mathematical Problem: Fundamental Theorem of Homomorphisms for Modules**
In all these problems, let \( R \) be any ring and \( M \) and \( N \) be \( R \)-modules.
1. **Theorem A**: If \( f : M \to N \) is an \( R \)-module epimorphism, **PROVE**:
\[
M/\text{Ker} f \cong N
\]
(this is the FHT for modules)
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