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 PrincipalIdeal 2013-03-22 11:51:49 2013-03-22 11:51:49 djao (24) djao (24) 7 djao (24) Definition msc 13A15 msc 16D25 msc 81-00 msc 82-00 msc 83-00 msc 46L05