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Nilpotent

In mathematics, an element x {\displaystyle x} of a ring R {\displaystyle R} is called nilpotent if there exists some positive integer n {\displaystyle n} such that x n = 0 {\displaystyle x^{n}=0} . The smallest such n {\displaystyle n} is called the index of nilpotency or the degree of nilpotency of x {\displaystyle x} .

Measurement, Nilpotency in physics & Commutative rings

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Overview

Examples

Properties

Commutative rings

Nilpotent elements in Lie algebra

Nilpotency in physics

Algebraic nilpotents

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Nilpotent

Nodes61
Edges60
Triples36
Avg. degree1.97
Density0.032787
Components1

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Nilpotent

Top relations

related to Examples · 10
Nilpotent → AB, An, Assume, BA, By, Here, In, The, Then, This
related to Commutative rings · 8
Nilpotent → As, Conversely, Every, If, So, The, This, Thus
related to Nilpotency in physics · 7
Nilpotent → An, Any, Fermionic, Grassmann, Pauli, The BRST, They
related to Nilpotent elements in Lie algebra · 5
Nilpotent → Jordan, Let, Lie, See, Then
related to Algebraic nilpotents · 3
Nilpotent → If, Other, The
related to Properties · 3
Nilpotent → All, An, No

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Important terminology

displaystyle ring element mathfrak prime elements ideal called algebra ideals commutative physics example unit nilradical lie also nilpotency idempotent definition

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Nilpotentrelated to Algebraic nilpotentsThe0.60section
Nilpotentrelated to Algebraic nilpotentsOther0.60section
Nilpotentrelated to Algebraic nilpotentsIf0.60section
Nilpotentrelated to Commutative ringsThe0.60section
Nilpotentrelated to Commutative ringsThis0.60section
Nilpotentrelated to Commutative ringsIf0.60section
Nilpotentrelated to Commutative ringsEvery0.60section
Nilpotentrelated to Commutative ringsSo0.60section
Nilpotentrelated to Commutative ringsConversely0.60section
Nilpotentrelated to Commutative ringsAs0.60section
Nilpotentrelated to Commutative ringsThus0.60section
Nilpotentrelated to ExamplesThis0.60section

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