Below are some examples of reduced rings.
A reduced ring is semiprime.
A ring is a domain (http://planetmath.org/CancellationRing) iff it is prime (http://planetmath.org/PrimeRing) and reduced.
Assume that is commutative, and let be the set of all nilpotent elements. Then is an ideal of , and that is reduced (for if , then , so , and consequently , is nilpotent, or ).
|Date of creation||2013-03-22 14:18:12|
|Last modified on||2013-03-22 14:18:12|
|Last modified by||CWoo (3771)|