Module factorisation theorem
From Maths
{{Stub page|grade=A*|msg=Todo:
- Quotient module
- Tidy up
- Add proof
Statement
Let (R,+,∗,0) be a ring (with or without unity) and let M be a (left) [[R-module|R-module}}. Let A be a submodule of A. Then[1]:
- for every homomorphism φ:M→B for some R-module B whose kernel contains A
- φ factors uniquely though the canonical projection π:M→MA
- That is to say there is a unique ψ:MA→B such that φ=ψ∘π
References