In mathematics, more specifically ring theory, a left, right or two-sided ideal of a ring is said to be a nil ideal if each of its elements is nilpotent.
The nilradical of a commutative ring is an example of a nil ideal; in fact, it is the ideal of the ring maximal with respect to the property of being nil. Unfortunately the set of nil elements does not always form an ideal for noncommutative rings. Nil ideals are still associated with interesting open questions, especially the unsolved Köthe conjecture.
Read more about Nil Ideal: Commutative Rings, Noncommutative Rings, Relation To Nilpotent Ideals
Famous quotes containing the words nil and/or ideal:
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—Friedrich Nietzsche (1844–1900)
“The contest between the Future and the Past is one between Divinity entering, and Divinity departing. You are welcome to try your experiments, and, if you can, to displace the actual order by that ideal republic you announce, of nothing but God will expel God.”
—Ralph Waldo Emerson (1803–1882)