# Ring problem with zero divisors

• May 8th 2010, 01:07 PM
ashamrock415
Ring problem with zero divisors
Does every ring with 1001 elements contain zero divisors?
• May 8th 2010, 01:46 PM
tonio
Quote:

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 $1001=7\cdot 11\cdot 13$ is not the power of a prime...

Tonio