Ring problem with zero divisors

May 2010
10
0
Does every ring with 1001 elements contain zero divisors?
 
Oct 2009
4,261
1,836
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