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May 14th, 2009, 09:28 PM   #1
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Commutative Diagram, Modules

Suppose



is a commutative diagram of modules over some ring . Suppose the rows are exact and and are bijective. Prove 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, 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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