Theorems · Theorem · commutative algebra

IsLocalRing.ResidueField.finite_of_finite

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : IsLocalRing R] [inst_2 : CommRing S]
  [inst_3 : IsLocalRing S] [inst_4 : Algebra R S] [IsLocalHom (algebraMap R S)] [Module.Finite R S],
  Finite (IsLocalRing.ResidueField R) → Finite (IsLocalRing.ResidueField S)

Defined in: Mathlib.RingTheory.LocalRing.ResidueField.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsLocalRing CommRing IsLocalRing Algebra IsLocalHom Module.Finite

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CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
RingHomstatement · cited by 10,189
Algebra.algebraMapstatement and proof · cited by 4,706
Finitestatement and proof · cited by 3,029
Module.Finitestatement and proof · cited by 1,032
IsLocalRingstatement and proof · cited by 339
IsLocalRing.ResidueFieldstatement and proof · cited by 156
IsLocalHomstatement and proof · cited by 100
Module.finite_of_finiteproof · cited by 8

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