Theorems · Theorem · ring theory

IsSemiprimaryRing.finite_of_isNoetherian

∀ (R₀ : Type u_1) (R : Type u_2) (M : Type u) [inst : Ring R₀] [inst_1 : Ring R] [inst_2 : Module R₀ R]
  [inst_3 : AddCommGroup M] [inst_4 : Module R₀ M] [inst_5 : Module R M] [IsScalarTower R₀ R M] [IsSemiprimaryRing R]
  [inst_8 : IsScalarTower R₀ R R] [Module.Finite R₀ (R ⧸ Ring.jacobson R)] [IsNoetherian R M], Module.Finite R₀ M

Defined in: Mathlib.RingTheory.HopkinsLevitzki
Cited by: 0 results in Mathlib
Foundations: Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Ring Ring Module AddCommGroup Module Module IsScalarTower IsSemiprimaryRing IsScalarTower Module.Finite IsNoetherian

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Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
Ringstatement and proof · cited by 7,463
Idealstatement · cited by 4,748
IsScalarTowerstatement and proof · cited by 3,896
HasQuotient.Quotientstatement and proof · cited by 2,301
Module.Finitestatement and proof · cited by 1,032
IsNoetherianstatement and proof · cited by 208
Ring.jacobsonstatement and proof · cited by 37
IsSemiprimaryRingstatement and proof · cited by 9

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