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 xboxlive89128 May 14th, 2009 08:40 PM

Commutative Diagram of Modules

Let $A$ be a ring. The following is a commutative diagram of $A-$module homomorphisms, and the rows are exact.

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

Suppose that $f_1$ is surjective and that $f_2$ is an isomorphism. Prove that $f_3$ is an isomorphism.

Attempt
Onto- $f_3= t \circ f_2$ and both $f_2$ and $t$ are both onto so $t \circ f_2$ 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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