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:
“Men have defined the parameters of every subject. All feminist arguments, however radical in intent or consequence, are with or against assertions or premises implicit in the male system, which is made credible or authentic by the power of men to name.”
—Andrea Dworkin (b. 1946)
“He will not idly dance at his work who has wood to cut and cord before nightfall in the short days of winter; but every stroke will be husbanded, and ring soberly through the wood; and so will the strokes of that scholar’s pen, which at evening record the story of the day, ring soberly, yet cheerily, on the ear of the reader, long after the echoes of his axe have died away.”
—Henry David Thoreau (1817–1862)