Radical Classes & Semi-Simple Classes of Rings

The concept of a radical was introduced by J. H. M. Wedderburn in 1908, for determination of structures of algebras and later on various radicals have been proposed by Artin, Baer, Jacobson, Brown-McCoy, Levitzki etc. for study of rings in the forties. The general theory of radicals was initiated by Kurosh (1953) and Amitsur in the early fifties. Andrunakievic, Sulinski, Divinsky and many others have followed up the works of Kurosh and Amitsur. The first example of a radical was the nilradical introduced in (Kthe 1930), based on a suggestion in (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 (Amitsur 1952, 1954, 1954b) and Kurosh (1953).