nilpotent element
Sign in to saveAlso known as nilpotent, nilpotency
In mathematics, an element x of a ring R is called nilpotent if there exists some positive integer n such that x^n=0. The smallest such n is called the index of nilpotency or the degree of nilpotency of x.
~5 min read
Encyclopedic overview
8 sectionsContents
- Examples
- Properties
- Commutative rings
- Nilpotent elements in Lie algebra
- Nilpotency in physics
- Algebraic nilpotents
- See also
- References
In mathematics, an element x of a ring R is called nilpotent if there exists some positive integer n such that x^n=0. The smallest such n is called the index of nilpotency or the degree of nilpotency of x.
The term, along with its sister idempotent, was introduced by Benjamin Peirce in the context of his work on the classification of algebras.
Excerpted from Wikipedia’s “nilpotent element” article, available under the CC BY-SA 4.0 licence.