principal ideal
PrincipalIdeal
2001-10-21 01:17:25
2002-10-24 17:48:48
Definition
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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 $(a)$.