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Canonical static concept record

Ordered ring

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Summary

A ring whose total order is compatible with addition and multiplication.

Record metadata

Carrier(s)

Data

Axioms / constraints

Concept sources

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Integers Z\mathbb ZOrdered ring

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

Authored explanation

Forgetting the canonical origin of its elements leaves the usual ordered-ring structure.

How to interpret this relation type

Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.

Relation sources

ring + total order(construction junction)Ordered ring

Permalink to relation

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

Authored explanation

Require addition and multiplication to respect the order.

How to interpret this relation type

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

Relation sources

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

No direct relations are authored in this direction.