# prime ring

A ring $R$ is said to be a prime ring if the zero ideal is a prime ideal.

If a prime ring $R$ is commutative, then it is a cancellation ring. If in $R$ has a multiplicative identity $1\neq 0$, then it is an integral domain.

Title prime ring PrimeRing 2013-03-22 11:51:05 2013-03-22 11:51:05 Wkbj79 (1863) Wkbj79 (1863) 10 Wkbj79 (1863) Definition msc 16U99 msc 16N60 ZeroIdeal