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I was reading this Lang's book where he says

F3: For every injection $0\rightarrow E'\rightarrow E$, we have $0\rightarrow E'\otimes F\rightarrow E\otimes F$

F1: For every exact sequence $E'\rightarrow E\rightarrow E''$, we have an exact sequence $E'\otimes F\rightarrow E\otimes F\rightarrow E''\otimes F$.

How do I show from F3 to F1? Lang says consider the kernel and image of the mapping $E'\rightarrow E$, but I couldn't figure out why. Thanks!

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    Tensor product is right exact, so F3 says that tensoring with flat modules preserves short exact sequences. Can you split up a 3-term exact sequence into some short exact sequences so that kernel and image can be analyzed?2012-11-06

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