Editing Radical of a ring (section)

===The Baer radical===
The Baer radical of a ring is the intersection of the [[prime ideal]]s of the ring ''R''. Equivalently it is the smallest [[semiprime ideal]] in ''R''. The Baer radical is the lower radical of the class of nilpotent rings.  Also called the "lower nilradical" (and denoted Nil<sub>∗</sub>''R''), the "prime radical", and the "Baer-McCoy radical".  Every element of the Baer radical is [[nilpotent]], so it is a [[nil ideal]].

For commutative rings, this is just the [[nilradical of a ring|nilradical]] and closely follows the definition of the [[radical of an ideal]].