Quote:

(ii) Let R be a PID and d is non_zero, non_unit. If R/(d) is indecomposable, show that d~p^n for some prime p in R.

Can you give me some hints how to do this question please?

Thank you so much

suppose $\displaystyle d$ has at least two distinct prime factors. let $\displaystyle p$ be a prime factor of $\displaystyle d.$ so we have $\displaystyle d=p^n a,$ where $\displaystyle \gcd(p,a)=1.$ therefore $\displaystyle <p^n> + <a>=R.$ see that $\displaystyle \frac{<p^n>}{<d>} \cap \frac{<a>}{<d>} = (0)$ and so