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Theorems · Inductive type · commutative algebra

IsDedekindRing

(A : Type u_2) → [CommRing A] → Prop

A Dedekind ring is a commutative ring that is Noetherian, integrally closed, and has Krull dimension at most one. This is exactly IsDedekindDomain minus the IsDomain hypothesis. The integral closure condition is independent of the choice of field of fractions: use isDedekindRing_iff to prove IsDedekindRing for a given fraction_map.

Defined in
Mathlib.RingTheory.DedekindDomain.Basic
Cited by
1 results in Mathlib
Foundations
Depth 1 from the axioms · uses no axioms
Assumes
CommRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsDedekindDomain.recOn · cited by 0IsDedekindDomain.recOnIsDedekindRing.casesOn · cited by 0IsDedekindRing.casesOnIsDedekindRing.recOn · cited by 0IsDedekindRing.recOnisDedekindRing_iff · cited by 0isDedekindRing_iffIsDedekindDomain.casesOn · cited by 0IsDedekindDomain.casesOnCommRing · cited by 17173CommRingIsDedekindRingCITED BYCITES

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Cited by5

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