# Thread: Ring problem with zero divisors

1. ## Ring problem with zero divisors

Does every ring with 1001 elements contain zero divisors?

2. Originally Posted by ashamrock415
Does every ring with 1001 elements contain zero divisors?

Yes, otherwise it'd be a field - a finite ring without zero divisors is a division ring and thus a field (this is not trivial!) - , but $\displaystyle 1001=7\cdot 11\cdot 13$ is not the power of a prime...

Tonio