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:
“Cows sometimes wear an expression resembling wonderment arrested on its way to becoming a question. In the eye of superior intelligence, on the other hand, lies the nil admirari spread out like the monotony of a cloudless sky.”
—Friedrich Nietzsche (1844–1900)
“It is equally impossible to forget our Friends, and to make them answer to our ideal. When they say farewell, then indeed we begin to keep them company. How often we find ourselves turning our backs on our actual Friends, that we may go and meet their ideal cousins.”
—Henry David Thoreau (1817–1862)