Theorems · Theorem · nonassociative algebras
RootPairing.rootForm_restrict_nondegenerate_of_ordered
∀ {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] [inst_4 : LinearOrder R] [IsStrictOrderedRing R] [inst_6 : Module R M]
[inst_7 : Module R N] (P : RootPairing ι R M N), LinearMap.Nondegenerate (P.RootForm.restrict (P.rootSpan R))See also RootPairing.rootForm_restrict_nondegenerate_of_isAnisotropic.
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- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
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- 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
- LinearOrderstatement and proof · cited by 8,572
- Fintypestatement and proof · cited by 7,736
- Submodulestatement · cited by 7,192
- IsStrictOrderedRingstatement and proof · cited by 2,490
- RootPairingstatement and proof · cited by 710
- RootPairing.rootSpanstatement · cited by 55
- RootPairing.RootFormstatement and proof · cited by 41
- LinearMap.Nondegeneratestatement · cited by 35
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