Theorems · Theorem · ring theory
TensorAlgebra.rank_eq
∀ {R : Type uR} {M : Type uM} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Nontrivial R]
[Module.Free R M],
Module.rank R (TensorAlgebra R M) = Cardinal.lift.{uR, uM} (Cardinal.sum fun n => Module.rank R M ^ n)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Cardinalstatement and proof · cited by 2,598
- Nontrivialstatement and proof · cited by 2,416
- Module.Basisproof · cited by 1,477
- Module.Freestatement and proof · cited by 597
- Cardinal.liftstatement and proof · cited by 583
- Module.rankstatement and proof · cited by 496
- AlgEquiv.toLinearEquivproof · cited by 117
- TensorAlgebrastatement and proof · cited by 81
- Cardinal.sumstatement and proof · cited by 58
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