Nilpotent
Element in a ring whose some power is 0 / From Wikipedia, the free encyclopedia
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This article is about a type of element in a ring. For the type of group, see Nilpotent group. For the type of ideal, see Nilpotent ideal. For the type of semigroup, see Nilpotent semigroup. For the type of algebra, see Nilpotent algebra.
In mathematics, an element of a ring is called nilpotent if there exists some positive integer , called the index (or sometimes the degree), such that .
The term, along with its sister idempotent, was introduced by Benjamin Peirce in the context of his work on the classification of algebras.[1]