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 May 14th, 2009, 08:28 PM #1 Newbie   Joined: Nov 2008 Posts: 25 Thanks: 0 Commutative Diagram, Modules Suppose is a commutative diagram of modules over some ring $R$. Suppose the rows are exact and $g$ and $h$ are bijective. Prove $f$ is bijective. Attempt: I know the snake lemma and five lemma. This looks more like a diagram chasing question. In the five lemma and snake lemma I can use the commutativity of the diagram, but here, $f$ is on the left, so I don't know how to use the commutativity of the diagram. Any hints for showing this would be nice. Thanks.

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