Module factorisation theorem

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{{Stub page|grade=A*|msg=Todo:

  1. Quotient module
  2. Tidy up
  3. 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:MB for some R-module B whose kernel contains A
    • φ factors uniquely though the canonical projection π:MMA
    • That is to say there is a unique ψ:MAB such that φ=ψπ

References

  1. Jump up Abstract Algebra - Pierre Antoine Grillet