principal ideal

Let $R$ be a ring and let $a\in R$. 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 ideal 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