Theorems · Definition · commutative algebra
RingEquiv.euclideanDomain
{R : Type u_1} → {S : Type u_2} → [inst : EuclideanDomain R] → [inst_1 : CommRing S] → S ≃+* R → EuclideanDomain SIf S is a nontrivial commutative ring isomorphic to a Euclidean domain
R then it is also a Euclidean domain.
- Defined in
- Mathlib.Algebra.EuclideanDomain.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- EuclideanDomainCommRing
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Nontrivialproof · cited by 2,416
- RingEquivstatement and proof · cited by 1,147
- RingEquiv.symmproof · cited by 567
- EuclideanDomainstatement and proof · cited by 124
- EuclideanDomain.rproof · cited by 13
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