I'm to prove that an ideal $M$ is primary iff for some $n$, $M = (p^n)$ where $p$ is a prime or $p=0$.
The second direction is simply proved referring to the definition of the primary ideal, my problem is in the first direction starting that $M$ is a primary ideal.
I have no idea to conclude that my ideal have to be generated by $p ^ n$.
Shall anybody help me ?
Hint:
$M=(a)$ for some $a\in R$ of course. Now suppose that $a$ has two distinct prime divisors. Can you use this to produce two nonzero elements $x,y$ such that $xy\in (a)$, and yet no powers of $x$ and no powers of $y$ are in $(a)$?
If you're having trouble with that hint, just try looking at what happens in $(pq)$ when $p,q$ are distinct primes.