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Algebraic structure

In mathematics, an algebraic structure or algebraic system consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities (known as axioms) that these operations must satisfy.

Common axioms, Common algebraic structures & Hybrid structures

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Overview

Introduction

Common axioms

Common algebraic structures

Hybrid structures

Universal algebra

Category theory

Different meanings of "structure"

Advanced semantic analysis

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Map overview Semantic statistics

Algebraic structure

Nodes128
Edges127
Triples63
Avg. degree1.98
Density0.015625
Components1

How this topic connects Entity context

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Algebraic structure

Top relations

related to Hybrid structures · 12
Algebraic structure → Algebraic, Archimedean, Banach, Hilbert, If, Lie, Neumann, Normed, Ordered, The, Topological, Vertex
related to Universal algebra · 12
Algebraic structure → Algebraic, An, Given, Identities, If, One, So, T/E, The, These, Thus, Universal
related to Category theory · 8
Algebraic structure → Category, Every, For, In, Likewise, Mac Lane, There, This
related to Existential axioms · 8
Algebraic structure → Also, Choosing, For, Given, In, More, Some, The
related to Introduction · 7
Algebraic structure → Addition, For, Many, Sets, Such, These, When
related to Non-equational axioms · 5
Algebraic structure → Every, It, Such, The, This
related to Different meanings of "structure" · 3
Algebraic structure → For, In, We
related to Equational axioms · 3
Algebraic structure → An, Here, If
related to One set with operations · 2
Algebraic structure → Set, Simple

Important terminology Word statistics

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Important terminology

algebraic structure operations algebra structures axioms operation group set category called multiplication ring universal field space variety commutative example collection

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
additioninstance oftypically binary operations0.80text
multiplicationinstance oftypically binary operations0.80text
fields have some axioms that hold only for nonzero members of Sinstance ofStructures0.80text
Algebraic structurerelated to Category theoryCategory0.60section
Algebraic structurerelated to Category theoryMac Lane0.60section
Algebraic structurerelated to Category theoryEvery0.60section
Algebraic structurerelated to Category theoryIn0.60section
Algebraic structurerelated to Category theoryFor0.60section
Algebraic structurerelated to Category theoryThis0.60section
Algebraic structurerelated to Category theoryLikewise0.60section
Algebraic structurerelated to Category theoryThere0.60section
Algebraic structurerelated to Different meanings of "structure"In0.60section

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    Min side: 3
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