\begin{definition}[Definition:Jacobson Radical]
Let $R$ be a commutative ring with unity.
Let $\map {\operatorname{maxspec}} R$ be the set of maximal ideals of $R$.
Then the '''Jacobson radical''' of $R$ is:
:$\ds \map {\operatorname{maxspec}} R = \bigcap_{m \mathop \in \map {\operatorname{maxspec}} R} m$
That is, it is the intersection of all maximal ideals of $R$.
\end{definition}