Editing Radical of a ring (section)

===The Artinian radical===
The Artinian radical is usually defined for two-sided [[Noetherian ring]]s as the sum of all right ideals that are [[Artinian module]]s.  The definition is left-right symmetric, and indeed produces a two-sided ideal of the ring.  This radical is important in the study of Noetherian rings, as outlined by {{harvtxt|Chatters|Hajarnavis|1980}}.
<!-- ===The Thierrin radical===
The Thierrin radical is the upper radical of all [[division ring]]s. It is hereditary.

===The Jenkins radical===
The Jenkins radical is the upper radical of all simple prime rings.
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