7
$\begingroup$

For $A$-modules and homomorphisms $0\to M'\stackrel{u}{\to}M\stackrel{v}{\to}M''\to 0$ is exact. Prove if $M'$ and $M''$ are fintely generated then $M$ is finitely generated.

  • 2
    Do this for vector spaces. Then do exactly the same for modules.2012-11-11
  • 2
    See the proof of the lemma of my answer to this question. http://math.stackexchange.com/questions/231058/noetherian-rings-and-modules2012-11-11

2 Answers 2