Standard Lemma guide
Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.
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adj
Such that, for some positive integer n, xn = 0.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Qualifier: ring theory
Topics: algebra, mathematics, sciences
Synonyms: none provided
Antonyms: none provided
adj
In any of several technical senses: behaving analogously to nilpotent ring elements as an element of some other algebraic structure; composed of elements displaying such behavior.
Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Qualifier: Lie theory
Topics: algebra, mathematics, sciences
No example sentence was provided for this meaning.
Synonyms: none provided
Antonyms: none provided
adj
In any of several technical senses: behaving analogously to nilpotent ring elements as an element of some other algebraic structure; composed of elements displaying such behavior.
Such that the lower central series terminates.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Qualifier: Lie theory
Topics: algebra, mathematics, sciences
No example sentence was provided for this meaning.
Synonyms: none provided
Antonyms: none provided
adj
In any of several technical senses: behaving analogously to nilpotent ring elements as an element of some other algebraic structure; composed of elements displaying such behavior.
Admitting a central series of finite length.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Topics: algebra, group-theory, mathematics, sciences
No example sentence was provided for this meaning.
Synonyms: none provided
Antonyms: none provided
adj
In any of several technical senses: behaving analogously to nilpotent ring elements as an element of some other algebraic structure; composed of elements displaying such behavior.
Such that there exists a natural number k with Ik = 0.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Qualifier: ring theory
Topics: algebra, mathematics, sciences
No example sentence was provided for this meaning.
Synonyms: none provided
Antonyms: none provided
adj
In any of several technical senses: behaving analogously to nilpotent ring elements as an element of some other algebraic structure; composed of elements displaying such behavior.
Containing only nilpotent elements.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Qualifier: semigroup theory
Topics: algebra, mathematics, sciences
No example sentence was provided for this meaning.
Synonyms: none provided
Antonyms: none provided
adj
In any of several technical senses: behaving analogously to nilpotent ring elements as an element of some other algebraic structure; composed of elements displaying such behavior.
Such that there exists some natural number n (called the index of the algebra) such that all products (of elements in the given algebra) of length n are zero.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Topics: algebra, mathematics, sciences
No example sentence was provided for this meaning.
Synonyms: none provided
Antonyms: none provided
noun
A nilpotent element.
Definition source: English Wiktionary via Wiktextract
Topics: algebra, mathematics, sciences
No example sentence was provided for this meaning.
Synonyms: none provided
Antonyms: none provided
adjective
equal to zero when raised to a certain power
Definition source: Princeton WordNet 3.0
No example sentence was provided for this meaning.
Synonyms: none provided
Antonyms: none provided
History
From nil (“not any”) + potent (“having power”) with literal meaning “having zero power” - bearing Latin roots nil and potens. Coined in 1870, along with idempotent, by American mathematician Benjamin Peirce to describe elements of associative algebras.
Across languages
8 source translations are retained for this English entry.
