Theorems · Theorem · commutative algebra
Module.Finite.of_isLocalization
∀ (R : Type u_3) (S : Type u_4) {Rₚ : Type u_1} {Sₚ : Type u_2} [inst : CommSemiring R] [inst_1 : CommSemiring S]
[inst_2 : CommSemiring Rₚ] [inst_3 : CommSemiring Sₚ] [inst_4 : Algebra R S] [inst_5 : Algebra R Rₚ]
[inst_6 : Algebra R Sₚ] [inst_7 : Algebra S Sₚ] [inst_8 : Algebra Rₚ Sₚ] [IsScalarTower R S Sₚ]
[IsScalarTower R Rₚ Sₚ] (M : Submonoid R) [IsLocalization M Rₚ] [IsLocalization (Algebra.algebraMapSubmonoid S M) Sₚ]
[hRS : Module.Finite R S], Module.Finite Rₚ Sₚ- Cited by
- 10 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetproof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- Submonoidstatement and proof · cited by 3,086
- Submodule.spanproof · cited by 1,504
- Module.Finitestatement and proof · cited by 1,032
- Finset.imageproof · cited by 910
Cited by10
Results whose statement or proof uses this declaration.
- Algebra.algebraMap_intTraceproof · cited by 4
- Algebra.trace_quotient_eq_of_isDedekindDomainproof · cited by 3
- differentIdeal_eq_differentIdeal_mul_differentIdealproof · cited by 3
- pow_sub_one_dvd_differentIdealproof · cited by 2
- Algebra.algebraMap_intTrace_fractionRingproof · cited by 2
- not_dvd_differentIdeal_of_intTrace_not_memproof · cited by 1
- RingHom.finite_localizationPreservesproof · cited by 1
- Algebra.intTrace_eq_of_isLocalizationproof · cited by 1
- Algebra.algebraMap_intNorm_of_isGaloisproof · cited by 1
- Algebra.dvd_algebraMap_intNorm_selfproof · cited by 1