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.

Title	prime element
Canonical name	PrimeElement
Date of creation	2013-03-22 12:46:52
Last modified on	2013-03-22 12:46:52
Owner	drini (3)
Last modified by	drini (3)
Numerical id	7
Author	drini (3)
Entry type	Definition
Classification	msc 13C99
Classification	msc 16D99
Synonym	prime
Related topic	PrimeIdeal
Related topic	DivisibilityInRings
Related topic	DivisibilityByPrimeNumber