Theorems · Theorem · commutative algebra

Algebra.trace_quotient_mk

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [Module.Free R S]
  [Module.Finite R S] [inst_5 : IsLocalRing R] (x : S),
  (Algebra.trace (R ⧸ IsLocalRing.maximalIdeal R) (S ⧸ Ideal.map (algebraMap R S) (IsLocalRing.maximalIdeal R)))
      ((Ideal.Quotient.mk (Ideal.map (algebraMap R S) (IsLocalRing.maximalIdeal R))) x) =
    (Ideal.Quotient.mk (IsLocalRing.maximalIdeal R)) ((Algebra.trace R S) x)

Defined in: Mathlib.RingTheory.Trace.Quotient
Cited by: 1 results in Mathlib
Foundations: Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing CommRing Algebra Module.Free Module.Finite IsLocalRing

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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
RingHom.idstatement · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommMonoidproof · cited by 12,281
Algebrastatement and proof · cited by 11,388
LinearMapstatement · cited by 10,215
RingHomstatement · cited by 10,189
Fintypeproof · cited by 7,736
Idealstatement · cited by 4,748
Algebra.algebraMapstatement and proof · cited by 4,706
Matrixproof · cited by 4,303
HasQuotient.Quotientstatement and proof · cited by 2,301

Cited by1

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Algebra.trace_quotient_eq_of_isDedekindDomainproof · cited by 3