Let $R$ be a Noetherian ring having an embedded associated prime $P$. If $a\in R$ is a non-zero divisor with $∩_{n=1}^\infty (a^n)=0$ I want to show that $R/(a)$ also has an embedded associated prime.
I know that $a$ does not belong to any associated prime of the zero ideal, so it does not to $P$. If no associated prime of $R/(a)$ is embedded then all have the form $Q/(a)$ where $Q$ is a minimal prime ideal of $R$ containing $(a)$... .
Any help to continue would be appreciated!