Prove that every ring without non-zero divisors can be embedded in a ring with identity which has no non-zero divisors.
I am not sure what we have to do here. In particular, I do not know the formal definition of an embedding. Wikipedia mentions the following definition for fields
In field theory, an embedding of a field $E$ in a field $F$ is a ring homomorphism $\sigma:E \to F.$
But here I have a ring. Can use this definition?