Primitive ideal
id:
primitive-ideal-295-772027
title:
Primitive ideal
text:
In mathematics, specifically ring theory, a left primitive ideal is the annihilator of a (nonzero) simple left module. A right primitive ideal is defined similarly. Left and right primitive ideals are always two-sided ideals. Primitive ideals are prime. The quotient of a ring by a left primitive ideal is a left primitive ring. For commutative rings the primitive ideals are maximal, and so commutative primitive rings are all fields.
brand slug:
wiki
category slug:
encyclopedia
description:
Annihilator of a simple module
original url:
https://en.wikipedia.org/wiki/Primitive_ideal
date created:
date modified:
2023-08-12T19:00:16Z
main entity:
{"identifier":"Q7243577","url":"https://www.wikidata.org/entity/Q7243577"}
image:
fields total:
13
integrity:
14