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Unital associative algebra

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Summary

An associative algebra with a multiplicative identity compatible with the base scalar action.

Record metadata

Carrier(s)

Data

Axioms / constraints

Notes

A multiplicative identity, if it exists, is unique; unitality is an existence condition on the associative multiplication.

Concept sources

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

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

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

Unital associative algebraCommutative unital algebra over a field

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

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

Unital associative algebraalgebra + coalgebra compatibility(construction junction)

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

Authored explanation

Supply multiplication and unit on the common carrier.

How to interpret this relation type

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

Relation sources