flatness problem: every exact seq of modules remain exact upon tensor product by X

27 Views Asked by At

I have to prove the following statements are equivalent

  1. If $f:A \to B$ is a monomorphism of $R-$modules, so is $i\otimes f$
  2. Every exact sequence of R-modules remains exact upon the tensor product by X

I don’t know how to prove $2\to 1 \cdots$