PlanetMath: prime ring

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prime ring

(Definition)

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

If a prime ring is commutative, then it is a cancellation ring. If in addition 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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Cross-references: integral domain, multiplicative identity, cancellation ring, commutative, prime ideal, zero ideal, ring
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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 3297 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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