Ideal of definition
= Ideal of definition
An ideal $I$ of a <Noetherian local ring> $(A,\mathfrak m)$ is an ideal of definition when $A/I$ has <Krull dimension> zero. Equivalently, $I$ is <primary ideal>[$\mathfrak m$-primary], so $\sqrt I=\mathfrak m$ and $\mathfrak m^r\subseteq I$ for some <positive integer> $r$.