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prime ring (Definition)

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 addition $R$ has a multiplicative identity $1 \neq 0$ , then it is an integral domain.



"prime ring" is owned by Wkbj79. [ full author list (2) | owner history (1) ]
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See Also: zero ideal
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Cross-references: integral domain, multiplicative identity, cancellation ring, commutative, prime ideal, zero ideal, ring
There are 3 references to this entry.

This is version 5 of prime ring, born on 2001-10-20, modified 2007-11-10.
Object id is 413, canonical name is PrimeRing.
Accessed 4003 times total.

Classification:
AMS MSC: 16N60 (Associative rings and algebras :: Radicals and radical properties of rings :: Prime and semiprime rings)
 16U99 (Associative rings and algebras :: Conditions on elements :: Miscellaneous)
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