Let $R$ be a commutative ring and let $0→A→B→C→0$ be an exact sequence of $R$ module. In general, for any $R-$module $N$,$A \otimes_R N→B \otimes_R N$・・・① is not always injective,
My question is, if $C$ is flat $R-$module, can we say ① is always injective ? I'm stuck with how to use flatness and exactness to prove ① is injective. If this is a famous fact, reference(book, pdf,etc・・・) is also appreciated.