Theorems · Theorem · nonassociative algebras

LieModule.exists_isRegular_of_finrank_le_card

∀ (R : Type u_1) (L : Type u_3) (M : Type u_4) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : Module.Finite R L] [inst_4 : Module.Free R L] [inst_5 : AddCommGroup M] [inst_6 : Module R M]
  [inst_7 : LieRingModule L M] [inst_8 : LieModule R L M] [inst_9 : Module.Finite R M] [inst_10 : Module.Free R M]
  [IsDomain R], ↑(Module.finrank R M) ≤ Cardinal.mk R → ∃ x, LieModule.IsRegular R M x

Defined in: Mathlib.Algebra.Lie.Rank
Cited by: 0 results in Mathlib
Foundations: Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing LieRing LieAlgebra Module.Finite Module.Free AddCommGroup Module LieRingModule LieModule Module.Finite Module.Free IsDomain

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Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Cardinalstatement · cited by 2,598
IsDomainstatement and proof · cited by 2,196
Module.finrankstatement and proof · cited by 1,770
LieRingstatement and proof · cited by 1,548
LieAlgebrastatement and proof · cited by 1,246
Module.Finitestatement and proof · cited by 1,032
Cardinal.mkstatement and proof · cited by 942
LieRingModulestatement and proof · cited by 727
Module.Freestatement and proof · cited by 597

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