SOLUTION: Let f: M to N be an R-module homomorphism and h: M to M/kerf be a natural homomorphism. Then prove that there exists a unique homomorphism g: M/kerf to N such that f=goh.

Question 1179187: Let f: M to N be an R-module homomorphism and h: M to M/kerf be a natural homomorphism. Then prove that there exists a unique homomorphism g: M/kerf to N such that f=goh.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

It is one of the first basic theorems related to homomorphisms of modules.

Students learn it from lectures in the basic course of Abstract Algebra, and it is written in any basic textbook on Abstract Algebra
in its relevant chapter related to Modules.

So, take your textbook and learn it from there.

By the way, which University you are, who is your professor and what is your basic textbook (name; author's name; edition; ISBN) ?

Please let me know.

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