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 May 14th, 2009, 08:40 PM #1 Newbie   Joined: Nov 2008 Posts: 25 Thanks: 0 Commutative Diagram of Modules Let $A$ be a ring. The following is a commutative diagram of $A-$module homomorphisms, and the rows are exact. 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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