prime element

An element p in a ring R is a prime elementMathworldPlanetmath if it generates a prime idealMathworldPlanetmath. If R is commutative, this is equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath to saying that for all a,bR , if p divides ab, then p divides a or p divides b.

When R= 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