Prove that, if $R$ is Noetherian, then so is each homomorphic image of $R$.
I know that by the Fundamental Homomorphism Theorem this is the same as showing that if $R$ is Noetherian, then so is $R/I$ for each proper ideal $I$, which I think I can use the correspondence theorem for this.
I am struggling piecing together how to write the proof though. Any help would be great!