Theorems · Theorem · commutative algebra
IsLocalization.away_of_isUnit_of_bijective
∀ {R : Type u_4} (S : Type u_5) [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Algebra R S] {r : R},
IsUnit r → Function.Bijective ⇑(algebraMap R S) → IsLocalization.Away r S- Cited by
- 6 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsUnitstatement and proof · cited by 1,602
- Function.Bijectivestatement and proof · cited by 863
- IsLocalization.Awaystatement · cited by 218
- IsUnit.mapproof · cited by 104
- IsUnit.submonoidproof · cited by 56
- Algebra.algebraMapSubmonoid_powersproof · cited by 9
- IsLocalization.of_le_isUnit_of_bijectiveproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- RingHom.LocalizationAwayPreserves.respectsIsoproof · cited by 4
- RingHom.IsStandardOpenImmersion.of_bijectiveproof · cited by 2
- Algebra.IsStandardOpenImmersion.of_bijectiveproof · cited by 1
- RingHom.StableUnderCompositionWithLocalizationAway.respectsIsoproof · cited by 1
- IsLocalization.Away.mul_of_isUnitproof · cited by 0
- IsLocalization.Away.mul_of_isUnit'proof · cited by 0