Definition:Jacobson Radical

Definition
Let $R$ be a commutative ring with unity.

Let $\operatorname{maxspec} \left({R}\right)$ be the set of maximal ideals of $R$.

Then the Jacobson radical of $R$ is:
 * $\displaystyle \operatorname{Jac} \left({R}\right) = \bigcap_{m \mathop \in \operatorname{maxspec} \left({R}\right)} m$

That is, it is the intersection of all maximal ideals of $R$.

Also denoted as
Some sources use $J \left({R}\right)$.