High Quality Content by WIKIPEDIA articles! In ring theory, a branch of mathematics, a radical of a ring is an ideal of "bad" elements of the ring. The first example of a radical was the nilradical introduced in (Kothe 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). In the theory of radicals, rings are usually assumed to be associative, but need not be commutative and need not have an identity element. In particular, every ideal in a ring is also a ring.

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