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Canonical static concept record

Commutative unital algebra over a field

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Summary

A unital associative algebra over a fixed field whose multiplication is commutative.

Record metadata

Canonical name: Commutative unital algebra over a field
Concept ID: commutative_algebra
Content version: 2.3.0
Primary field: Mathematics
Fields: Mathematics
Primary domain: Algebra
Domains: Algebra, Algebraic geometry
Alternate terminology: No alternate terminology is currently authored for this record.

Carrier(s)

unital associative algebra $A$

Axioms / constraints

$ab=ba$

Notes

“Commutative algebra” also names the subject. This node denotes an individual commutative unital algebra over the scalar field inherited from the algebra branch.

Concept sources

Wikipedia — Associative algebra — Associative algebra · expository · source ID wp-associative-algebra
nLab — Associative algebra — Associative algebra · reference · source ID nlab-associative-algebra
Wikipedia — Commutative algebra — Commutative algebra · expository · source ID wp-commutative-algebra
Stacks Project — Commutative Algebra (PDF) — Commutative Algebra (PDF) · reference text · source ID stacks-algebra-text

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Unital associative algebra Commutative unital algebra over a field

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: e_unital_commalg
Relation type: Impose axiom impose-axiom
Direction: source → target
Endpoint roles: source: Builds toward; target: Built from
Authored annotation: + commutativity

Authored explanation

Require multiplication to commute.

How to interpret this relation type

Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.

Relation sources

Wikipedia — Associative algebra — Associative algebra · expository · source ID wp-associative-algebra
nLab — Associative algebra — Associative algebra · reference · source ID nlab-associative-algebra
Wikipedia — Commutative algebra — Commutative algebra · expository · source ID wp-commutative-algebra
Stacks Project — Commutative Algebra (PDF) — Commutative Algebra (PDF) · reference text · source ID stacks-algebra-text

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

No direct relations are authored in this direction.

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