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Division ring

In algebra, a division ring, also called a skew field, is a nontrivial ring in which division by nonzero elements is defined. Specifically, it is a nontrivial ring in which every nonzero element a has a multiplicative inverse; that is, an element usually denoted a–1, such that a a–1 = a–1 a = 1. So, (right) division may be defined as a / b = a b–1, but…

Relation to fields and linear algebra, Examples & Related notions

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Relation to fields and linear algebra

Examples

Main theorems

Related notions

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Map overview Semantic statistics

Division ring

Nodes49
Edges48
Triples31
Avg. degree1.96
Density0.040816
Components1

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Division ring

Top relations

related to Relation to fields and linear algebra · 10
Division ring → All, Doing, Gaussian, If, In, Matrices, Much, Schur's, So, The
related to Examples · 7
Division ring → As, If, Laurent, Let, The, This, When
related to Main theorems · 5
Division ring → All, Ernst Witt, Frobenius, The, Wedderburn's
related to Related notions · 5
Division ring → Division, English, In, The, Thus
is a · 1
Division ring → field

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Important terminology

division ring rings fields field commutative quaternions every noncommutative module used skew defined algebra right one called nontrivial center algebras

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Division ringis afield0.90text
quasideterminants allow some resultsinstance ofalthough generalizations0.80text
the octonions are also of interest.A near-field is an algebraic structure similar to a division ringinstance ofnonassociative division algebras0.80text
except that it has only one of the two distributive lawsinstance ofnonassociative division algebras0.80text
Division ringrelated to ExamplesAs0.60section
Division ringrelated to ExamplesThe0.60section
Division ringrelated to ExamplesWhen0.60section
Division ringrelated to ExamplesLet0.60section
Division ringrelated to ExamplesLaurent0.60section
Division ringrelated to ExamplesIf0.60section
Division ringrelated to ExamplesThis0.60section
Division ringrelated to Main theoremsWedderburn's0.60section

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