Theorems · Theorem · commutative algebra
Algebra.weaklyQuasiFiniteAt_iff
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (q : Ideal S)
[inst_3 : q.IsPrime],
Algebra.WeaklyQuasiFiniteAt R q ↔
Algebra.QuasiFinite R (Localization.AtPrime q ⧸ Ideal.map (algebraMap R (Localization.AtPrime q)) (Ideal.under R q))- Defined in
- Mathlib.RingTheory.QuasiFinite.Weakly
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites45
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idproof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Ringproof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- AlgHomproof · cited by 3,236
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Ideal.IsPrimestatement and proof · cited by 827
- RingHomClass.toRingHomproof · cited by 746
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.WeaklyQuasiFiniteAt.of_algHom_localizationproof · cited by 1
- Algebra.WeaklyQuasiFiniteAt.of_quasiFiniteAt_residueFieldproof · cited by 1