principal ideal

Let R be a ring and let aR. The principal left (resp. right, 2-sided) ideal of a is the smallest left (resp. right, 2-sided) ideal of R containing the element a.

When R is a commutative ring, the principal idealMathworldPlanetmathPlanetmathPlanetmathPlanetmath of a is denoted (a).

Title principal ideal
Canonical name PrincipalIdeal
Date of creation 2013-03-22 11:51:49
Last modified on 2013-03-22 11:51:49
Owner djao (24)
Last modified by djao (24)
Numerical id 7
Author djao (24)
Entry type Definition
Classification msc 13A15
Classification msc 16D25
Classification msc 81-00
Classification msc 82-00
Classification msc 83-00
Classification msc 46L05