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xboxlive89128 May 14th, 2009 08:40 PM

Commutative Diagram of Modules
 
Let be a ring. The following is a commutative diagram of module homomorphisms, and the rows are exact.

http://i719.photobucket.com/albums/w...nghu21/2-1.png

Suppose that is surjective and that is an isomorphism. Prove that is an isomorphism.

Attempt
Onto- and both and are both onto so is onto.
1-1- This one doesn't seem as trivial. I am a bit confused on showing this.

Thanks in advance for any hints.


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