An element $p$ in a ring$R$ is a prime element if it generates a prime ideal. If $R$ is commutative, this is equivalent to saying that for all $a,b \in R$ , if $p$divides$ab$ , then $p$ divides $a$ or $p$ divides $b$ .
When $R = \mathbb{Z}$ the prime elements as formulated above are simply prime numbers.
This is version 4 of prime element, born on 2002-06-12, modified 2004-04-24.
Object id is 3094, canonical name is PrimeElement.
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