I am beginner in algebra. I want to know if every power of a prime ideal is a principal ideal. Is the statement correct or is there a counterexample?
Power of prime ideal
2
$\begingroup$
abstract-algebra
-
3Hint (because this looks like homework): It would be enough to find a ring with a prime ideal that is not principal. – 2011-12-20
-
0@HenningMakholm Why did you delete it, I was thinking the same.. was it something wrong in that? – 2011-12-20
-
1@AD: the last sentence of the question as originally asked sounded to me like a translation from a homework exercise in some non-English language -- so I decided I'd rather not provide a complete solution. – 2011-12-20
-
0@HenningMakholm Ok I agree. – 2011-12-20
-
1Vahid: Start by looking at a *non-PID*. – 2011-12-20
-
0So, Vahid, why do you ask did you try anyting? – 2011-12-20
-
0@AD. No problem. And I'm somehow surprised that you were able to summon me based on just the edit. I didn't know that was possible. So at least I learned something from this occasion. – 2011-12-20
-
2Vahid, please try to use a respective language. – 2011-12-20