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 (Köthe 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).
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Famous quotes containing the words radical and/or ring:
“Our conscience is not the vessel of eternal verities. It grows with our social life, and a new social condition means a radical change in conscience.”
—Walter Lippmann (1889–1974)
“It is engend’red in the eyes,
With gazing fed; and fancy dies
In the cradle where it lies.
Let us all ring fancy’s knell.
I’ll begin it—Ding, dong, bell.”
—William Shakespeare (1564–1616)