Nil Ideal

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 K├Âthe 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 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 (1859–1930)