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Canonical static concept record

Reduced scheme

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Summary

A scheme whose local rings contain no nonzero nilpotents.

Record metadata

Carrier(s)

Axioms / constraints

Concept sources

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

SchemeReduced scheme

Permalink to relation

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

Authored explanation

Require no nonzero nilpotents in local rings.

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.

Reduced schemeIntegral scheme

Permalink to relation

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

Authored explanation

Require the reduced scheme to be nonempty and irreducible.

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