Editing Radical of a ring (section)

{{Short description|Ideal ring structure}}
In [[ring theory]], a branch of [[mathematics]], a '''radical of a ring''' is an [[ideal (ring theory)|ideal]] of "not-good"{{definition needed|date=March 2025}} elements of the [[ring (mathematics)|ring]].

The first example of a radical was the [[nilradical of a ring|nilradical]] introduced by {{harvtxt|Köthe|1930}}, based on a suggestion of {{harvtxt|Wedderburn|1908}}. In the next few years several other radicals were discovered, of which the most important example is the [[Jacobson radical]]. The general theory of radicals was defined independently by {{harvs|last=Amitsur|year1=1952|year2=1954|year3=1954b}} and {{harvtxt|Kurosh|1953}}. <!-- maybe the German translation of his 1944 book Teoriya Grupp ? -->

The study of radicals is called '''torsion theory'''.