Theorems · Theorem · commutative algebra
Algebra.IsStandardSmoothOfRelativeDimension.of_algebraMap_bijective
∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S],
Function.Bijective ⇑(algebraMap R S) → Algebra.IsStandardSmoothOfRelativeDimension 0 R S- Defined in
- Mathlib.RingTheory.Smooth.StandardSmooth
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement and proof · cited by 4,706
- Function.Bijectivestatement and proof · cited by 863
- Algebra.IsStandardSmoothOfRelativeDimensionstatement · cited by 17
- Algebra.Presentation.ofBijectiveAlgebraMap_dimensionproof · cited by 2
- Algebra.SubmersivePresentation.ofBijectiveAlgebraMapproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- RingHom.IsStandardSmoothOfRelativeDimension.equivproof · cited by 2