Theorems · Theorem · nonassociative algebras

LieAlgebra.exists_isRegular_of_finrank_le_card

∀ (R : Type u_1) (L : Type u_3) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : Module.Finite R L] [inst_4 : Module.Free R L] [IsDomain R],
  ↑(Module.finrank R L) ≤ Cardinal.mk R → ∃ x, LieAlgebra.IsRegular R x

Defined in: Mathlib.Algebra.Lie.Rank
Cited by: 1 results in Mathlib
Foundations: Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing LieRing LieAlgebra Module.Finite Module.Free IsDomain

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Cites13

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CommRingstatement and proof · cited by 17,173
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
Module.Freestatement and proof · cited by 597
LieModule.toEndproof · cited by 144
LieHom.toLinearMapproof · cited by 74
LieAlgebra.IsRegularstatement · cited by 7

Cited by1

Results whose statement or proof uses this declaration.

LieAlgebra.exists_isCartanSubalgebra_engel_of_finrank_le_cardproof · cited by 1