PlanetMath: prime element

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prime element

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An element in a ring is a prime element if it generates a prime ideal. If is commutative, this is equivalent to saying that for all $a,b \in R$ , if divides , then divides or divides .

When $R = \mathbb{Z}$ the prime elements as formulated above are simply prime numbers.

"prime element" is owned by drini. [ full author list (2) | owner history (2) ]

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Other names:

prime

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Cross-references: divides, equivalent, commutative, prime ideal, generates, ring
There are 27 references to this entry.

This is version 4 of prime element, born on 2002-06-12, modified 2004-04-24.
Object id is 3094, canonical name is PrimeElement.
Accessed 5441 times total.

Classification:

AMS MSC:	13C99 (Commutative rings and algebras :: Theory of modules and ideals :: Miscellaneous)
	16D99 (Associative rings and algebras :: Modules, bimodules and ideals :: Miscellaneous)

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