Theorems · Theorem · nonassociative algebras
RootPairing.disjoint_rootSpan_ker_rootForm
∀ {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], Disjoint (P.rootSpan R) (LinearMap.ker P.RootForm)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Submodulestatement and proof · cited by 7,192
- Disjointstatement and proof · cited by 2,201
- IsDomainstatement and proof · cited by 2,196
- le_reflproof · cited by 2,061
- Module.finrankproof · cited by 1,770
- LinearMap.kerstatement · cited by 848
Cited by5
Results whose statement or proof uses this declaration.
- RootPairing.isCompl_rootSpan_ker_rootFormproof · cited by 4
- RootPairing.eq_zero_of_mem_rootSpan_of_rootForm_self_eq_zeroproof · cited by 2
- RootPairing.rootForm_nondegenerateproof · cited by 1
- RootPairing.disjoint_corootSpan_ker_corootFormproof · cited by 0
- RootPairing.rootForm_restrict_nondegenerate_of_orderedproof · cited by 0