Example of ring such that the nil radical is prime and 0 is not

Question

I was just trying to think about an example of a ring that is not a domain and the nilradical is prime, however I could not find anyone.

Thanks in advance.

score 4 · Accepted Answer · answered May 24 '13 at 00:25

4

$\mathbb{Z} / 4 \mathbb{Z}$ works.

answered May 24 '13 at 00:25

user79202

Any prime power works. – lhf May 24 '13 at 00:35
It was easier than I thought. I tried to pick rings with only one prime ideal. – user40276 May 24 '13 at 00:38

1 Answers1