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Associative algebra

In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center of A. This is thus an algebraic structure with an addition, a multiplication, and a scalar multiplication (the multiplication by the image of the ring homomorphism of an element of K). The addition and…

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Overview

Definition

Algebra homomorphisms

Examples

Constructions

Enveloping algebra

Separable algebra

Finite-dimensional algebra

Lattices and orders

Related concepts

Representations

Non-unital algebras

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Associative algebra

Nodes145
Edges144
Triples101
Avg. degree1.99
Density0.013793
Components1

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Associative algebra

Top relations

related to Algebra · 19
Associative algebra → Any, Categorically, Cuntz, EndR, Every, Given, If, In, Quillen, R-algebra, R-module, RX, The, Therefore, This, Z-algebra, Z-algebras, Z-modules, Z/nZ
related to As a monoid object in the category of modules · 10
Associative algebra → By, For, Indeed, Pushing, R-algebra, R-bilinear, R-linear, R-Mod, R-modules, The
related to Dual of an associative algebra · 9
Associative algebra → For, Hence, Hopf, However, Let, Representations, Since, The, Then
related to Geometry and combinatorics · 8
Associative algebra → Brauer, For, Incidence, Omega, Rham, Temperley-Lieb, The, The Clifford
related to Mathematical physics · 8
Associative algebra → Dual, Gerstenhaber, Given, If, Leibniz, Lie, Poisson, The
related to Representations · 8
Associative algebra → End, Here, Hopf, However, If, Imposing, Lie, The
related to Algebra homomorphisms · 7
Associative algebra → A1, A2, Explicitly, R-Alg, R-algebras, R-linear, The
related to Coalgebras · 7
Associative algebra → An, F-coalgebra, If, K-vector, There, These, This
related to Representation theory · 7
Associative algebra → Hopf, If, It, Lie, Many, R-algebra, The
related to Analysis · 6
Associative algebra → Azumaya, Banach, Ft, Given, The, The Weyl

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Important terminology

algebra ring associative commutative homomorphism multiplication structure also product space center algebras r-algebra tensor field example category module given form

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
the exteriorinstance ofThe same is true for quotients0.80text
symmetric algebrasinstance ofThe same is true for quotients0.80text
Associative algebrarelated to AlgebraAny0.60section
Associative algebrarelated to AlgebraZ-algebra0.60section
Associative algebrarelated to AlgebraThe0.60section
Associative algebrarelated to AlgebraTherefore0.60section
Associative algebrarelated to AlgebraZ-algebras0.60section
Associative algebrarelated to AlgebraZ-modules0.60section
Associative algebrarelated to AlgebraZ/nZ0.60section
Associative algebrarelated to AlgebraGiven0.60section
Associative algebrarelated to AlgebraR-module0.60section
Associative algebrarelated to AlgebraEndR0.60section

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