Theorems · Theorem · nonassociative algebras
RootPairing.finrank_rootSpan_map_polarization_eq_finrank_corootSpan
∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : Fintype ι] [inst_1 : AddCommGroup M]
[inst_2 : AddCommGroup N] [inst_3 : CommRing R] [IsDomain R] [inst_5 : Module R M] [inst_6 : Module R N]
(P : RootPairing ι R M N) [P.IsAnisotropic],
Module.finrank R ↥(Submodule.map P.Polarization (P.rootSpan R)) = Module.finrank R ↥(P.corootSpan R)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Fintypestatement and proof · cited by 7,736
- Submodulestatement and proof · cited by 7,192
- IsDomainstatement and proof · cited by 2,196
- Module.finrankstatement and proof · cited by 1,770
- LinearMap.rangeproof · cited by 893
- RootPairingstatement and proof · cited by 710
- Submodule.mapstatement and proof · cited by 614
- RootPairing.rootSpanstatement and proof · cited by 55
Cited by1
Results whose statement or proof uses this declaration.
- RootPairing.disjoint_rootSpan_ker_rootFormproof · cited by 5