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Associative algebra

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Summary

An algebra over a commutative base ring or field whose multiplication is associative.

Record metadata

Carrier(s)

Data

Axioms / constraints

Concept sources

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Algebra over a fieldAssociative algebra

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

Authored explanation

Require (ab)c=a(bc)(ab)c=a(bc).

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

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

Associative algebracomplete normed algebra(construction junction)

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

Authored explanation

Supply an associative algebra over the same normed field KK, on the same carrier, addition, and scalar action as the Banach space.

How to interpret this relation type

Feed several structures into a construction junction and impose compatibility between them.

Relation sources

Associative algebra*-algebra

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

Authored explanation

Over a scalar field with involution, add a semilinear involutive anti-automorphism.

How to interpret this relation type

Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.

Relation sources

Associative algebraUnital associative algebra

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

Authored explanation

Select associative algebras whose multiplication has a two-sided identity; it is unique.

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