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Suppose $R$ is a commutative ring, $f\colon F_1\to F_2$ is a homomorphism of free modules, and $M$ is an $R$-module.

If $f$ is a surjective homomorphism, then $f\otimes_R \mathrm{id}_M$ is surjective.

Is it true that if $f$ is a monomorphism, then $f\otimes_R \mathrm{id}_M$ is a monomorphism? I can't think of any counterexamples.

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    Please write your questions so that the *complete* question is in the body. Your previous question was editing by someone else, but you can do it yourself... (And there is no need for abreviations like «comm.»: you are not charged by the character!)2011-02-03
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    Commenting so that this will be visible at the top: This question is Problem 1.5 on the homework for Math 620, at the University of Buffalo. As user "Student" points out, every question user6560 has asked is a homework question from that course. http://www.math.buffalo.edu/~badzioch/MTH620/Homework_files/hw1.pdf2011-02-13

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