Theorems · Theorem · commutative algebra
RingHom.IsStandardOpenImmersion.of_bijective
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] {f : R →+* S},
Function.Bijective ⇑f → f.IsStandardOpenImmersionA bijective ring map is a standard open immersion.
- Defined in
- Mathlib.RingTheory.RingHom.OpenImmersion
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- RingHomstatement and proof · cited by 10,189
- Function.Bijectivestatement and proof · cited by 863
- isUnit_oneproof · cited by 48
- RingHom.IsStandardOpenImmersionstatement · cited by 12
- IsLocalization.away_of_isUnit_of_bijectiveproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- RingHom.IsStandardOpenImmersion.respectsIsoproof · cited by 1
- RingHom.IsStandardOpenImmersion.idproof · cited by 1