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Affine scheme

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Summary

A locally ringed space isomorphic to Spec(R)\operatorname{Spec}(R) for a commutative ring RR.

Record metadata

Carrier(s)

Axioms / constraints

Concept sources

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Commutative ringAffine scheme

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

Authored explanation

The functor Spec\operatorname{Spec} gives an anti-equivalence between commutative rings and affine schemes; morphisms reverse direction.

How to interpret this relation type

Reinterpret an object, pass to an equivalent presentation, or relate canonically corresponding structures; the carrier may change.

Relation sources

Prime spectrum Spec(R)\operatorname{Spec}(R)Affine scheme

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

Authored explanation

An affine scheme is precisely a locally ringed space isomorphic to Spec(R)\operatorname{Spec}(R) for some commutative ring.

How to interpret this relation type

Reinterpret an object, pass to an equivalent presentation, or relate canonically corresponding structures; the carrier may change.

Relation sources

SchemeAffine scheme

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

Authored explanation

Require the scheme to be isomorphic to Spec(R)\operatorname{Spec}(R) for some commutative ring RR.

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

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No direct relations are authored in this direction.