Let A be a right R-module. Suppose for every left ideal J of R, the homomorphism $f:A\otimes J\to A$ defined by $f(x\otimes y)=xy$ is injective, then A is a flat R-module.(the identity 1 is in R)
I found the result in my book but didn't give me the proof, and I felt very confused about it! Can someone tell me how to prove it?