Theorems · Theorem · commutative algebra
RingTheory.Sequence.IsWeaklyRegular.isRegular_of_isLocalizedModule_of_mem
∀ {R : Type u_1} (S : Type u_2) {M : Type u_3} {N : Type u_4} [inst : CommRing R] [inst_1 : CommRing S]
[inst_2 : Algebra R S] [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : AddCommGroup N] [inst_6 : Module R N]
[inst_7 : Module S N] [IsScalarTower R S N] (p : Ideal R) [inst_9 : p.IsPrime] [IsLocalization.AtPrime S p]
[Nontrivial N] [Module.Finite S N] (f : M →ₗ[R] N) [IsLocalizedModule.AtPrime p f] {rs : List R},
RingTheory.Sequence.IsWeaklyRegular M rs →
(∀ r ∈ rs, r ∈ p) → RingTheory.Sequence.IsRegular N (List.map (⇑(algebraMap R S)) rs)- Defined in
- Mathlib.RingTheory.Regular.Flat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement and proof · cited by 10,215
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- Nontrivialstatement and proof · cited by 2,416
Cited by1
Results whose statement or proof uses this declaration.
- RingTheory.Sequence.IsWeaklyRegular.isRegular_of_isLocalization_of_memproof · cited by 0