Theorems · Theorem · commutative algebra
IsLocalRing.finrank_quotient_map
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
[inst_3 : IsLocalRing R] [Module.Finite R S] [Module.Free R S],
Module.finrank (R ⧸ IsLocalRing.maximalIdeal R) (S ⧸ Ideal.map (algebraMap R S) (IsLocalRing.maximalIdeal R)) =
Module.finrank R S- Defined in
- Mathlib.RingTheory.LocalRing.Quotient
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Top.topproof · cited by 9,680
- Idealstatement · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- Set.rangeproof · cited by 4,705
- HasQuotient.Quotientstatement and proof · cited by 2,301
- le_antisymmproof · cited by 2,068
- Module.finrankstatement and proof · cited by 1,770
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalRing.finrank_eq_finrank_residueFieldproof · cited by 1