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.
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 (18441900)
“The ideal reasoner, he remarked, would, when he had once been shown a single fact in all its bearings, deduce from it not only all the chain of events which led up to it but also all the results which would follow from it.”
—Sir Arthur Conan Doyle (18591930)