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# prime element

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.

Related:

PrimeIdeal, DivisibilityInRings, DivisibilityByPrimeNumber

Synonym:

prime

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

13C99*no label found*16D99

*no label found*

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## Corrections

use \mid not | by djao ✓

no caps by rmilson ✓

fewer symbols by rmilson ✓

divides != divisible by by igor ✓

Classification by archibal ✓

no caps by rmilson ✓

fewer symbols by rmilson ✓

divides != divisible by by igor ✓

Classification by archibal ✓