Show that a principal ideal in a polynomial ring has no embedded associated primes.

On the other hand, if $\displaystyle R=k[x_1,x_2,x_3,x_4]/<x_1x_4-x_2x_3,x_2^3-x_1^2x_3,x_3^3-x_2x_4^2>$

show that the principal ideal $\displaystyle <x_2>\subset R$ has embedded associated primes.