### What does **nilpotent** mean?

# Definitions for nilpotent

nilpo·tent

#### This dictionary definitions page includes all the possible meanings, example usage and translations of the word **nilpotent**.

### Princeton's WordNet

nilpotentadjective

equal to zero when raised to a certain power

### Wiktionary

nilpotentadjective

Describing an element, of a ring, for which there exists some positive integer n such that x = 0.

### ChatGPT

nilpotent

In mathematics, nilpotent refers to an element of a mathematical structure which becomes "zero" when raised to a certain positive power. Specifically, in a ring (a set with two operations, typically labeled as addition and multiplication), an element, 'a', is called nilpotent if there exists a positive integer 'n' such that a^n = 0. The term is also used in various other mathematical contexts with slightly different definitions. For example, in linear algebra, a square matrix is nilpotent if some power of it equals the zero matrix. In group theory, a group is nilpotent if it has an ascending sequence of normal subgroups whose factors are all abelian. Despite their differences, all definitions of nilpotency express the core idea of exponential diminishment.

### Wikidata

Nilpotent

In mathematics, an element x of a ring R is called nilpotent if there exists some positive integer n such that x = 0. The term was introduced by Benjamin Peirce in the context of elements of an algebra that vanish when raised to a power.

### Usage in printed sources**From:**

- [["1890","5"],["1893","1"],["1908","2"],["1918","3"],["1919","12"],["1927","7"],["1931","172"],["1936","1"],["1939","3"],["1940","18"],["1941","1"],["1942","20"],["1943","17"],["1944","1"],["1945","12"],["1947","44"],["1948","21"],["1949","55"],["1950","46"],["1951","16"],["1952","13"],["1953","63"],["1954","20"],["1955","174"],["1956","262"],["1957","120"],["1958","6"],["1959","39"],["1960","244"],["1961","11"],["1962","105"],["1963","143"],["1964","38"],["1965","87"],["1966","143"],["1967","64"],["1968","102"],["1969","23"],["1970","106"],["1971","88"],["1972","138"],["1973","301"],["1974","249"],["1975","189"],["1976","770"],["1977","63"],["1978","54"],["1979","57"],["1980","276"],["1981","87"],["1982","94"],["1983","86"],["1984","151"],["1985","300"],["1986","253"],["1987","214"],["1988","160"],["1989","292"],["1990","167"],["1991","225"],["1992","1980"],["1993","366"],["1994","280"],["1995","369"],["1996","186"],["1997","503"],["1998","242"],["1999","423"],["2000","341"],["2001","419"],["2002","550"],["2003","442"],["2004","314"],["2005","250"],["2006","337"],["2007","761"],["2008","296"]]

### Numerology

Chaldean Numerology

The numerical value of nilpotent in Chaldean Numerology is:

**6**Pythagorean Numerology

The numerical value of nilpotent in Pythagorean Numerology is:

**8**

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"nilpotent." *Definitions.net.* STANDS4 LLC, 2024. Web. 18 Sep. 2024. <https://www.definitions.net/definition/nilpotent>.

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