Theorems · Theorem · ring theory
FreeAlgebra.rank_eq
∀ (R : Type u) (X : Type v) [inst : CommRing R] [Nontrivial R],
Module.rank R (FreeAlgebra R X) = Cardinal.lift.{u, v} (Cardinal.mk (List X))- Defined in
- Mathlib.LinearAlgebra.FreeAlgebra
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 and proof · cited by 2,598
- Nontrivialstatement and proof · cited by 2,416
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.liftstatement and proof · cited by 583
- Module.rankstatement and proof · cited by 496
- Cardinal.lift_idproof · cited by 163
- FreeMonoidproof · cited by 147
- Cardinal.lift_umaxproof · cited by 56
- FreeAlgebrastatement and proof · cited by 48
- FreeAlgebra.basisFreeMonoidproof · cited by 2
- Module.Basis.mk_eq_rank'proof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- TensorAlgebra.rank_eqproof · cited by 0
- Algebra.rank_adjoin_leproof · cited by 0