Theorems · Theorem · commutative algebra
Algebra.Generators.sq_ker_comp_le_ker_compLocalizationAwayAlgHom
∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} {ι : Type u_4} [inst : CommRing R] [inst_1 : CommRing S]
[inst_2 : Algebra R S] [inst_3 : CommRing T] [inst_4 : Algebra R T] [inst_5 : Algebra S T]
[inst_6 : IsScalarTower R S T] (g : S) [inst_7 : IsLocalization.Away g T] (P : Algebra.Generators R S ι),
((Algebra.Generators.localizationAway T g).comp P).ker ^ 2 ≤
RingHom.ker (Algebra.Generators.compLocalizationAwayAlgHom T g P)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites49
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 and proof · cited by 10,189
- Finsuppstatement · cited by 5,255
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- AlgHomstatement · cited by 3,236
- HasQuotient.Quotientstatement and proof · cited by 2,301
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.Generators.liftBaseChange_injective_of_isLocalizationAwayproof · cited by 2